First, you need to get some stuff to practice with. In the past I find that scrub nurses/techs can be very helpful in helping you acquire different sutures to practice with that are going to be disposed of anyway. Please keep in mind that many of the specialty sutures can cost $3-8 or more per strand so stealing a whole bunch from your hospital is not a good thing. Likewise needle-drivers etc cost over $100/piece so ask before taking and if you do take, at least bring them back when you don't need them anymore.
Now to your question: practicing.
Models:
The traditional thing to practice on is a pig's foot. You can get them at the supermarket, they aren't very expensive. Cut through the skin with a sharp knife and practice closing that way. For more realistic practice cut out an ellipse and close that so there is some tension.
I preferred whole chickens which are often also very cheap to buy and have more fascial planes deeper to practice on as well, but the skin is very flimsy and take a little more skill to get closed well.
I have also heard of people practicing on oranges on the rind. Can't say that I've tried this myself but it makes sense as phlebomotists often used to use these as models for blood draw practice.
Things to learn: You should be able to get the description from any surgery book so I'll focus on what you should look for as you practice. If you are looking for one with a good chapter, I recommend Chassin's Operative Strategy in General Surgery (it's about $150 so I'd see if your library has it and just photocopy the chapter, unless you plan to be a general surgeon in which case it's invaluable as a 1st atlas)
Opening and closing the needle driver. Practice. Nothing makes you look more like you know what you are doing than something who handles the instruments with confidence. Also, nothing runs a perfect stitch faster than being rough as you try to let go of the needle. Put one in your pocket and open and close it until it annoys your friends. Practice with your fingers in the holes and not in the holes (different attendings will prefer one or the other). Also practice loading needles about 1/2 to 2/3 of the way back on the curve of the needle.
Simple stitch. Practice by marking the two spots with a marker that you want to hit first to improve your needle control.
Simple baseball stitch. Start with this as it is easiest to learn. Focus on getting your stitches even in width and distance between them. This will help perfect your needle control. These are things that will serve you well when doing all other stitches.
Subcuticular stitch. The most common closing stitch that a student will be allowed to do. Practice finding the right plane just beneath the skin making sure not to penetrate the skin itself as you are making your stitch. Focus on getting your stitches straight across from one another, this will make the skin not gap and bunch making it look beautiful. To improve this, before you cut the skin you want to sew close, draw hash marks perpendicular to the planned incision and make sure you are matching stuff up.
Deep dermal stitch. Again, focus on getting exactly the right plane. If you do this stitch right, it'll seem like you don't even have to close the skin at that place.
Vertical and Horizontal mattresses. once you can do the above things, this will seem like a snap. You probably want to get someone to give you a live demonstration of one of these once, because sometimes the book descriptions don't really explain how these are placed well.
Good luck! Have fun practicing!
