So you have a number of choices to make. You can,
|   | As you can see it is easy to accrue many different tools but you really don't need this many to start. In the picture you'll see a combination of different mallets, straight, toothed or rounded chisels, and a couple of files (to sound professional call them rifflers). | 
I finished the first seven of my works without ever reading about stone carving. However I did get instructions from professor, artist, mentor and friend, Bill Kolok. Therefore I attribute all information here that I did not learn by trial and error, to him.
|   | These are what the different basic chisels look like in a starter set. I have shown them in the order you will probably use them along with a riffler and a file. | 
|   | If I don't have an idea of what I want the piece to look like I just start carving. This can be the hardest way to go since you don't know where you're going with it. You can make it easier by giving yourself a "quick start". Take a drill with a masonry bit and drill a couple of holes in it. Then build your shapes around the holes. You'll be amazed how that will help to give you a starting point. | 
|   | If I know what I'm going to carve, I usually start out by making a rough drawing of my idea. Then I find a piece of stone that fits the design as close as possible. The reason for this is you want to keep the amount of stone to be removed to a minimum. I make a drawing on the stone itself and rough it out. Do not use a marker or pen with any kind of ink in it. I did this on one of my sculptures and it bled several centimeters into the stone. If you cannot remove a lot of stone you'll have a permanent smear to explain to your viewing public (mine is blue). Use pencil or crayon. | 
The point chisel is held about a 45 degree angle to the stone. This will vary according to the hardness of the stone. The harder the stone, the steeper the angle has to be. Don't try to take out too much stone at a time. The object here is to make a line in stone with the first pass. Successive passes will make the line deeper. Make additional lines about 1 to 1.5 inches apart. Then make more lines in a crosshatch pattern. This leaves squares of stone that can be easily knocked off with a chisel. As you make the lines and remove stone it should start to take on a shape.
Don't just follow the contours of the stone since all that will happen is the stone will get smaller and smaller. Instead try to accentuate the stone. Make the low points a lot lower while leaving the high points high. I have observed in the art classes I attended that this is very hard for some people to do. Do not be afraid to go for it. It is only a rock UNTIL you shape it. After the rough shape has emerged you use the next chisel (called a claw chisel) to further refine the shape and to remove the lines left by the point. This is where you start to get excited, things are taking shape.
Once you have removed the lines left by the point and have roughed out the shape using the claw you can use the toothed chisel to remove the lines left by the claw. See what's happening? Each step is designed to further smooth the stone. For marble it is very important to follow these steps. For the softer stones such as soapstone you may skip back and forth as seems best. For example, I do not like using the claw on soapstone and go from the point right to the toothed.
Now the flat chisel comes into play. This is the chisel that will save you a lot of work later if done right. The flat chisel is used to remove the lines of the toothed chisel ONLY. If you try to remove stone with it you will chip off pieces and the surface will not be smooth (This can be a desirable effect if you want to texture a softer stone this way, experiment on a scrap piece to see what happens).
The reason this chisel will save you work is because the next tool to use is a rasp or a riffler. These are used to smooth out the final chisel marks and to carve out fine detail that the chisels are too course for. They are not for removing mass amounts of stone although inexperienced carvers often use them this way. These tools are designed to work in one direction only (forwards) and a "seesaw action" will only wear you out and cause your tool to dull prematurely.
Next comes the file. One of my favorites is available at any hardware stone as a wood rasp. It has course and rough, flat and rounded sides. I have worn a couple of them out but they are inexpensive and one of my favorites. Use the file to (again) remove the rasp or riffler marks.
At this time you may see some white spots in the stone. These may be bruises and can only be removed by chiseling or rasping deeper into the stone, which may change the shape. Its better to be careful while chiseling to avoid them.
Now comes the lousy part, sanding. This can take quite a bit of time but don't give up. The results will be worth it.
Start with a course grade (100 grit) of a silicon carbide (wet and dry) sandpaper, diamond paper is best but it is about $30.00 a sheet. Next in order go to 150 grit, 200 grit, 300 grit, 400 grit..... until its the smoothness you desire. I have gone up to 1600 grit to get the desired finished. Sometimes a high gloss is not what looks the best so experiment and see what happens. When sanding make sure you remove all scratches left by the previous paper or when you go to the next finer grit you may not be able to (or at the very least it will take much more work). Once you get to the 200 grit (with soapstone you'll have to start around 150 grit) it is best to use wet sanding. Get a shallow pan of water, dip the paper in it (you have to have waterproof sandpaper) and sand. As the paper gets clogged wash it and the stone off and repeat. The water keeps the paper from clogging up. Change the water frequently and always when you go to a finer grit since the water will contain the courser grit and will keep scratching the stone.
Another plus to the water is that it will give you an idea of what the stone will look like when polished.
I have found that 3M paper does very well with this kind of strain on it. I have tried others but they didn't hold up as well. Now that the sanding is done there is a number of steps you can take. Some people buy a rouge which is available through some of the suppliers I have listed and use a buffing wheel on a drill to apply it. If you do this, keep that wheel separate from your final buffing wheel. After the sanding make sure the stone is thoroughly dry. Some stones dry quickly and some like limestone can take a day or two. You can then apply a wax, also available through suppliers or use a floor wax made from carnauba wax. This is a hard wax and seems to do well. Rub it with your fingers until some of it melts on them and then rub it into the stone. Try to rub it hard enough to warm the stone to allow the wax to penetrate. If the stone is cold (and small enough) you may put it in a oven on warm. Don't cook it, just warm it. After applying the wax buff it with a buffing wheel (guess where you get that from?) or hand buff it with a lint free cloth (cloth diapers work well for this). Be careful when using power buffers, you don't want to press too hard. A light pressure is fine and be sure to keep moving it around, don't hold it in one place. I get great pleasure in hand buffing if I have the time. There is something about feeling the stone warm up in your hands and seeing the shine come out as you work.
Limestone can be installed outside with no wax, but if you leave it inside and desire to wax it only one brand of wax that I have found will work well. It is available only though art suppliers. The brand name is Akemi stone polishing fluid 2012. This is a liquid that you wipe on and then buff. Works well on many stones but make sure you have adequate ventilation when using it as the fumes are bad while drying.
Marble takes an additional step. After sanding and rouge (if used) you have to seal the surface. This is done either with oxalic acid (order it from the local drug stone) or with tin oxide (availible from art suppliers). I use the acid. Dissolve it warm water until no more will dissolve. Use something like a rough piece of felt and rub the surface with it WEAR GLOVES AND GLASSES, this is an acid that will attack organic matter including your skin or eyes. It literally melts the surface crystals together to seal the marble. Wash off after a few minutes with water, let dry completely, then use the wax of your choice. Tin oxide also works but it takes a lot of rubbing to achieve the same effect. Save your sweat for later.
 Drill a hole (or holes if the sculpture is big enough) in the base of the sculpture.  I use a tool purchased from Sears for this.  It is a small portable device and your drill (3/8in. without the chuck attached) mounts to the top of it and the chuck is mounted underneath.  You set the tool's base flat on the stone  and it makes sure you drill it straight.  If the base of the stone is too small you can attach a piece of wood with a hole for the bit in it, to the tool.  This will let it set on a smaller area than the manufacturer provided for.  After the hole is in the stone, position a piece of paper on it.  Mark the outline of the stone and punch out the holes.  Put this paper on the base, line up the outlines and mark the position of the holes.  Using the drill tool, drill out the holes in the base.  This will ensure proper alignment of the holes.
Drill a hole (or holes if the sculpture is big enough) in the base of the sculpture.  I use a tool purchased from Sears for this.  It is a small portable device and your drill (3/8in. without the chuck attached) mounts to the top of it and the chuck is mounted underneath.  You set the tool's base flat on the stone  and it makes sure you drill it straight.  If the base of the stone is too small you can attach a piece of wood with a hole for the bit in it, to the tool.  This will let it set on a smaller area than the manufacturer provided for.  After the hole is in the stone, position a piece of paper on it.  Mark the outline of the stone and punch out the holes.  Put this paper on the base, line up the outlines and mark the position of the holes.  Using the drill tool, drill out the holes in the base.  This will ensure proper alignment of the holes.