Hands are the vital tools a boxer needs to use, and protect, in order to be successful. No matter whether your sparring, hitting your heavybag or just hitting the speedbag, you should ALWAYS wrap your hands prior to training. Wrapping your hands helps to protect the small bones on the top of the hand, the thumb, and also helps to support the wrists and protect the knuckles.
When wrapping, you want the handwrap to be snug, but not too tight, so occasionally make a fist while your wrapping and make sure it feels comfortable.
It will be hard to describe this process in words, but Ill do my best. Note that there are many different ways to wrap hands, but this is how I was taught at my gym and it seems to work very well for me.
When wrapping your hands, you want to start out with your palm facing the floor, and your fingers spread far apart. The reason your fingers must be spread apart is that you will prevent the handwrap from becoming too tight, and cutting off circulation.
Start with the loop of the thumb, and wrap across the back of the wrist. Wrap around the wrist about 3 times, then across the top of the hand and around covering the palm. Come up across the knucles twice, and then back underneath across the palm again. You want to then make 3 X's which would be across the top of the hand, and around the base of the thumb and across the lower palm of the hand, then back across the top of the hand to the front base of the thumb. Youll notice this makes an "X" across the top of the hand. After you make your 3 X's, loop across the base of the thumb once, and then get about 3 loops over the top of the knuckles. After that try and get one or two more X's if you have enough handwrap left, and finish off by getting a couple loops around the wrist for wrist security.
Some people will put small tape pieces inbetween the knuckles to prevent the handwrap from slipping over the top of the knuckles while in the glove. Some will even use the handwrap itself inbetween the knuckles to do the same thing. I didnt use either because i didnt need it, and when using handwrap inbetween, it was creating more pain in the joints of my knuckles after training. This I'll leave up to you and what works for you.
If you need a better illustration or instruction for wrapping hands, you can check out this instructional page from Ringside:
The Proper Way to Wrap Your Hands