There is more than one way to wrap your hands for boxing.
In addition to this one - the most basic method is good for anyone starting out. It is easy and provides good protection. That said, there is a better method, in my opinion, that offers even better protection and keeps the wraps in place over your knuckles a whole lot better. It takes a little getting used to as you will feel the wrap between your fingers, but the wrap will not slide off your knuckles even after the most rigourous session on the heavy bag.
You have a few different options for handwraps. At minimum you should get a set of 180" wraps. Some people prefer Mexican style handwraps. They are a bit more elastic and are supposed to offer better protection. At any rate, you have to purchase some kind of wrap for your hands. If you are thinking about buying the Everlast ones at Canadian Tire, don't. They are super short and don't offer much protection at all. Get yourself a decent set.
Method 2 (Video): How to Wrap Your Hands - Between the Fingers
Video or pictures, use what works best for you. Follow the pictures in the sequences below. Every number corresponds to a description below the sequence. Obviously this sequence is to wrap your left hand. To do your right, simply reverse everything.
I find that this method is far superior to the basic method when throwing uppercuts on the heavy bag. I've experienced more knuckle scrapes with the basic method and uppercuts than with this method. Overall, it is a tighter, more secure wrap. It's a little harder to master, but once you've got the hang of it, you're good to go.
1. One end of your hand wrap will have a thumb loop in it. Put your thumb through the loop as shown. Always keep your fingers spread wide apart or the wrapping job will be too tight in the end and you'll lose circulation in your hands. Bring the wrap diagonally towards your shoulder over the back side of your hand.
2. With palm facing away from you, bring the wrap down towards the floor (back side of wrist).
3. Wrap around your wrist and bring wrap up as shown in the picture.
4. Wrap twice more around your wrist for total of 3 wraps finishing with wrap towards the floor.
5. Bring the wrap diagonally across back of your hand towards outside of your pinky finger.
6. Wrap around outside of pinky across the palm side of knuckles with wrap towards the floor. Your palm is still away from you at this point.
7. Bring wrap up and across your knuckles.
8. Wrap around your knuckles, bringing the wrap diagonally across your palm, down towards your body.
9. Keeping the wrap taught, bring the wrap straight across back of your hand between your pinky and ring finger. You'll need to keep your thumb wide open so the wrap doesn't slide off. It will fold a bit between your fingers, this is okay.
10. Once through your fingers, bring it down and straight back towards your body again.
11. Now, take it straight back across back of your hand and pass it through the space between your ring finger and middle finger just like you did the pinky.
12. Once through your fingers, bring it down and straight back towards your body again (across palm of your hand).
13. One more time, bring the wrap straight across back of your hand and pass it through the space between your middle finger and index finger.
14. Once through, bring it down and straight back towards your body again.
15. Bring wrap diagonally across back of your hand towards the outside of your pinky.
16. Lock everything in place by bringing the wrap around your pinky, down towards the floor.
17 Continue locking everything in place by wrapping around your knuckles, finising with wrap pointing up.
18 Wrap around your knuckles again, finish with wrap towards floor.
19 Bring wrap diagonally across back of your hand towards your shoulder, passing it between thumb and index finger.
20. Pass around your wrist and point towards the floor.
21. Wrap around your thumb by bringing the wrap underneath your thumb and away from you.
22. Finish wrapping your thumb by pulling the wrap back towards you and the floor.
23. Bring it straight up across the back of your wrist, finishing upwards.
24. Wrap around your wrist, bringing the wrap straight back down.
25. Flip your hand over so palm is inwards and bring wrap diagonally across it to pass between thumb and index finger.
26. As it passes through rotate your hand so palm is away from you and bring wrap across back of your thumb.
27. Continue in that direction and pull the wrap down, around your wrist, then back towards the ceiling.
28. From there, you're going to do a series of figure 8's to wrap everything in place. So, bring wrap diagonally across back of hand to pass between thumb and index finger again.
29. Wrap once around your knuckles and end with wrap towards the ceiling.
30. Bring it down, around your wrist.
31. Bring wrap back up..
32. Now repeat the figure 8 pattern - passing it through your thumb and index finger.
33. Wrap once around your knuckles and end with wrap towards the ceiling.
34. Bring it down, across your knuckles.
35. Flip your hand so palm is up and bring the wrap diagonally across your palm towards your body.
36. Wrap around your wrist.
37. Wrap the remainder of the wrap around your wrist and attach the velcro to hold it securely in place. If you find that the velcro is on the wrong side, simply twist the hand wrap so it is right side up and then fasten it. The twist doesn't matter.
And finally, you have a finished product. Now switch hands and do the other one exactly the same way.
Like the basic method, wrapping your hands takes practice and it will be awhile before you get the hang of it. Just keep practicing and you'll get it eventually, and when you do, you'll be ready to hit something. Enjoy.