A few quick tips:
Make sure the tourniquet is on tight.
Drop the site below the level of the tourniquet to facilitate venous pooling.
Develop your feel for palpating veins. In obese and very dark African American patients, you may not visualize a vein at all, even when one is there.
Wrap the site/arm/leg with very warm blankets to dilate the veins if you have absolutely no target, with or without a tourniquet on. Don't leave a tourniquet on for more than five continuous minutes
When placing the IV, the most common early mistake is attempting to advance the catheter over the needle before enough of the catheter has entered the vein. If only a small portion of the catheter or no portion of the catheter has entered the vein and you try to advance the catheter, you will push the vein off of the needle and blow the vein.
Advance the unit until you get a flash of blood, then drop the entire unit 10-20 degrees and advance another 3-5 mm. You can then push the catheter off of the needle and into the vein. If the patient is experiencing great pain while you do this, you are likely not in the vein and have either pushed the vein off of the needle or pushed through the back wall of the vein and are advancing the catheter into soft tissue.
If you back wall the vein, you can sometimes salvage the IV by removing the needle, slowly withdrawing the catheter until you get blood flow again, at which point the distal tip should be back in the lumen of the vein. Unlike an artery, it is not a simple task to just advance the catheter or place a wire or the needle back through the catheter to serve as a guide. The vein will likely flip off the end of the catheter again or will have bled enough to become collapsed and not allow entry of the catheter (does not have the muscular wall of an artery that can stay circular). You can try to inject some saline through the catheter as you try to advance it, in order to reinflate the vein, but I have rarely seen that work unless you backwalled a large vein that you should have gotten in the first place.
Learn to use the fingers of your supporting to fix the vein in position by pinching/pressing it below where you intend to cannulate. This helps pin the "rolling" veins and fix their position under the skin.
Tapping the vein with your fingers about 10 times before you sterilize with alcohol and give local can also inflame and engorge the vein locally and make the vein more prominent as well.
Bending the entire unit by 10-15 degrees helps to prevent backwalling when you are trying to get forearm veins or veins on patients with obstructing body parts.
Know all of the common targets for PIV's, but also know where your best backups lie (saphenous leg vein, lateral wrist surface vein, cephalic vein, etc.).
Norm's sneaky trick for small and/or volume depleted veins: place a 22 or 24 ga IV as distally as possible in your target vein. Hook up a pig tail catheter or any catheter with a syringe and inject 5-10 cc's of fluid into the vein, WITH THE TOURNIQUET UP. Do this gently and with a stopcock and you will inflate/dilate the vein distal to the tip of the small catheter. You can then place a larger IV more proximally (relative to the patient, not the small catheter) in the now distended vein.
RIC catheters (Rapid infusion catheters) can also be placed by putting an 18 ga PIV into a large AC vein, threading a guidewire through the catheter, removing the catheter, using a knife to nick the skin, and advancing the RIC catheter over the wire using a Seldinger technique. Instant large bore IV.
REMEMBER TO REMOVE YOUR TOURNIQUET AFTER YOU HAVE PLACED YOUR CATHETERS!!!! I have seen junior residents leave tourniquets used to place IV's after the patient is asleep, on for the entire case, resulting in severe extremity edema secondary to poor venous drainage and aggressive flushing of fluid through an IV that is backing up for a reason. Nerve damage from iatrogenic compartment syndrome is not a good thing to have on your record.
There are many more tips/tricks, but these will get you through your first year.