If you need a tourniquet, a piece of 1/4 inch penrose drain tubing works really well. We keep a box with our IV supplies, and cut a piece a few inches long. Rubber bands are good for scalp IV's, keep scissors handy to cut it off when you have a flashback.
If you are new to this, always have someone help hold the baby. That can be half the battle, as it's much easier having help taping the IV in place.
Equipment is important, different size arm boards are helpful. We usually use plastic tape, but add either a folded 2x2 or a cotton ball dabbed on the sticky part which will prevent the tape from sticking too much to the upper arm or leg. We use Veniguards to cover the site, so the actual cath site is visible, but the IV is snug. We also use a short T-connector with a 5 ml syringe of saline attached start the IV, then connect the tubing with a Lever-lock. One place I worked didn't use those, I was really glad when we got them. I've seen people use a syringe of saline to float the catheter in, but then it has to be separated to attach the tubing.
We usually tape the babe's fingers together, I use a half inch wide strip of tape, maybe 2-3 inches long. It's easier to keep them in place like that, and you can still see that they are pink.
If you are using the hand, fold the baby's fingers to the palm, so you are holding the wrist and fingers, with the back of the hand in place. When you have prepped the site, go in at a very slight angle. Unless you have a 10lb chub, the veins are right below the surface. If the catheter won't advance when you have a flashback, attach the T-connecter and have your partner try to flush it in.
The saphenous vein inside the ankle is usually a good place to start, although you can't always see it. Start feeling for veins, often the big ones in the AC and the ankle can't be seen. Those skinny little veins on the foot will surprise you, if you see a straight one, go for it!
The last thing is the taping. Always leave the site visible, if you use Tegaderm or a Veniguard, or whatever, DON'T tape across it. If you can't see the cath insertion site, you can miss an infiltrate until it's a nasty problem. I tape the upper arm, then across the fingers, with usually two narrow strips of tape in an X so the thumb is free but the hand is down. Sometimes I'll put a narrow strip at the top of the Veniguard, and also across the hub, if a little pressure is needed.
OK, maybe you didn't need all that, the main thing is practice, practice. If you have someone in your dept that's good, watch what she does, and ask for suggestions. Good luck!