The bracelet is really cute - nice design with adorable materials - but in tutorial terms, I have to suggest a modification in technique to make the structure stronger. Right now it isn't really structurally sound, though this particular bracelet may not have pulled apart yet... I just worry that one good yank could rip it apart, and that would be a shame. So, here is the way to make this style more secure.
First of all, do not use eyepins. These are made to dangle things with. They're not meant to be used as part of the main structure of any item except earrings, IE in places where there might be stress on them, IE your bracelet gets caught on something as you walk by. The reason is that the loop is pretty easy to open if you tug on a chain made of eye pins. The wire of the loop needs to come back around and wrap the base at least once or twice to be stable enough to be a main component.
What you should use is beading wire, of a sturdy gauge (18? 21? up to you - it just has to work with the beads you're using, and not be too delicate). You'll probably need two sets of pliers; one can be the nylon-covered clamp pliers sold for use with wire jigs; use that to hold the wire (some will just hold it in their hand, which is fine). Wire cutters might also help. A file to use on a clipped wire end is handy; this can be anything from a proper metal jewelry file to an emery board that you'd use on your nails, but the metal file will work better.
1 - Clip out a section of beading wire a few inches long.
2 - Using a round-tip plier (as shown in the photos), bend the wire at an angle (also as shown), and continue to wrap the wire around one tip of the pliers, which you can do with your hand or the other pliers.
3 - Once you've made a circle, make sure one of the long ends is crossing over the other at about a right angle.
4 - At this point, you might choose to slip the ring of the last link or the next link into the loop, before you close the loop in step 5 by wrapping its base. If you have split rings - which aren't as stable as the unsplit rings that you can use with this technique - you don't need to worry about this step, but if you don't, and you ignore this step, you'll find yourself swearing and cutting open a lot of loops you've already finished, and throwing away wire, which sucks if you're working with sterling. I'm just saying.
5 - Continue wrapping the working end around the other end of wire at the base of the loop you've made. The wraps should go from close to the loop to further away. 2 wraps are usually sufficient.
6 - Trim the excess wire from the working end and, with your pliers, work it firmly to the bottom of the wraps. File its edge down so it doesn't stick out or catch on anything.
7 - Slip the bead onto the remaining end of the wire.
8 - Repeat earlier steps on the remaining end, making the loop fairly close to the other side of the bead (leaving enough room for wraps, but little more).
THINGS to pay attention to - how many wraps are at the base of each loop? In which direction do they go? These questions don't help with the stability of the work, but if you pay attention to them, your work will look more professional.
This is an elementary beading technique, so you can find it explained other places on the web if my explanation doesn't help - I think I might have worded it confusingly. Try here: http://jewelrymaking.about.com/library/weekly/aa111001.htm
. It can take a while to get right, but a bracelet in this style is usually just the ticket in terms of practice: I made 2 about ten years ago and have never had a problem since. Before you start, you can always make ten or twenty practice loops on cheap throwaway craft wire; if they work out, you can use them as eye pins in the future. Have fun!