Bracelets are tricky pieces of jewelry, since you can only use one hand to deal with many different types of clasps, fastenings and ties. However, all these techniques can be managed with the same principle without having to call over someone for assistance.
Hold one end of the bracelet in the hand that will not be wearing it. For clasped bracelets, hold the clasp and practice closing it. For non-clasped bracelets, hold the end that may need to be slipped through a loop on the other end. If both ends are identical, it doesn't matter which end you are holding.
Hold the arm that will wear the bracelet in front of you so that the inner arm faces you and the outer arm faces away.
Drape the bracelet around the wrist so that the other end (the one you are not holding) is on the outer side of the arm.
Brace your wrist against your body, so the clasp you were holding falls against your body and can be pulled up to meet the other end of the bracelet. This position will prevent the bracelet from slipping off your wrist while you're trying to tie it.
Attach the clasp or tie the two ends together. For the latter, you can do two starting knots (the first knot you use to tie your shoe laces) or a starting knot followed by a slipknot (a square knot, except one of the ends is pulled in as a loop through the hole).