You will need a clasp, stringing material, and everything else depends on what kind of clasp and what kind of stringing material you choose!
For heavy stuff like turquoise, I'd use tiger tail. This means you will need to use crimp beads to attach the clasp. There are speical pliers for crimping; I just use regular toothed pliers and squash the crimps flat, but this is very unprofessional and I shouldn't recommend it, even if it does work, saves buying andother pair of pliers and, to be honest, it doesn't look that bad either. *smirks*
If you want to just use beading thread, however, you will have to knot the thread onto the clasp and use French wire (aka lots of things) to protect it. I found a tute for that somewhere... http://beadwork.about.com/cs/beadshowtos/ht/frenchwire.htm
here it is!
Clasp-wise, it depends on what you prefer. There are loads of different types, and basically it depends whether you prefer security or want a decorative clasp. Barrels (aka screw clasps), lobster clasps (aka trigger clasps) and bolt rings (aka spring rings) are all pretty good, secure ways of fastening a necklace. Toggle clasps can be very pretty indeed, but they are not so secure IMO, and personally I wouldn't trust magnetic clasps at all, though some people adore them. Take note of how heavy your beads are.
The Beadalon website http://www.beadalon.com
has lots of information about stringing materials, beading and crimping under their FAQ section. Their catalogue has useful pictures of different types of clasp (page 29-31). Do bear in mind that they are trying to sell their own products, though, and your local craft shop probably has cheaper alternatives! They also have a lot of gadgets that you probably won't need, ever
For bead stringing you can pretty much stick with the crimping pliers, tool-wise. You need more for wire work but that's another rant entirely
I hope this hasn't confused you too much. It's not all as complicated as the explanation makes it sound! I really have to go now, but PM me with any further/more specific questions and I'll be happy to help!