For cutting, I mostly use an X-Acto razor saw for thicker pieces (course or fine blade, depending), and X-Acto or hobby knives for thin pieces. For sheets, You can score straight lines then snap your piece off.
As JTFazz said, model or plastic cement melts both parts, then has to be held or clamped together and forms a bond as it solidifies. Super glue is usually quicker, and there are various thicknesses depending on the application (bonding flat pieces, irregular pieces, or parts with gaps between the joins). Super glue, or CA, forms something like an acrylic bond between the pieces. I always score the parts being joined by cross-hatching with a hobby knife point. It gives the CA something to "grab onto" for a stronger bond. They also make accelerator that you apply to instantly harden the CA.
Check with your LOCAL hobby shops and craft stores first, then the modeling companies like Squadron.com. Evergreen put out a book on working with styrene that has all the info you need.