These take some practice, but you may find that these hand tools are, in certain situations, faster and more accurate than power tools.
There are two basic kinds of saws that you may find useful in your projects: regular western saws and Japanese pull-saws. Crosscut handsaws are good for rough cuts, and are sometimes faster than power tools. A dovetail or gent's saw is smaller with much finer teeth and a rigid back. it is used for delicate hand-cut joinery. Most western saws cut on the push stroke. This is less efficient and hard to control than Japanese saws which cut on the pull stroke (think how much hard it is to draw a straight line away from you than it is to draw one towards you). Like drill bits or chisels, if you are going to need a handsaw you may want to buy your own. A good saw can run you between $20-100, but will be money well spent.
Chisels are wonderful, ancient tools. Essentially knives, they need to be as sharp as possible to make smooth, fast cuts. Using a chisel takes quite a bit of practice, but the basics are fairly straight-forward. Always try to cut in the direction of the grain -- cutting across the grain can result in tearing. Always use a wooden or plastic mallet with a chisel. Never use a metal hammer -- it will damage the chisel and make a really annoying sound. To cut a mortise (a square hole in which a tenon -- peg -- goes), you first hold the chisel vertically, with the flat edge facing out. With a few strikes of the mallet, score the surface in all four directions. This cuts the grain across (to prevent tearing) and helps maintain straight edges. Then, holding the chisel at a 15-or-so degree angle and with the flat side up, cut with the grain until you reach the other side of mortise. You should make one nice curly shaving. Repeat this process until you reach the other side. For very thick pieces, it is advisable to cut through on one side, then halfway on the other. This results in the outside being tight with the tenon, avoiding unsightly gaps.
Doesn't initially seem suited for making cuts, but when used in conjunction with a jig you can rough cut your piece on the bandsaw, then remove the rest with the router, making repeated shapes quickly. The router can also be used to cut grooves (dados), round or bevel edges, and make decorative cuts. When routing, always follow the correct direction or the router may catch and throw itself. For cuts on the outside of the board, move the router counter-clockwise; inside move the router clockwise.
BELT / DISC SANDER and SPINDLE SANDER
Used more for shaping than sanding surfaces before finishing. The belt / disc sander can be used to square off ends or smooth curves cut on the bandsaw. The spindle sander works similarly, but is best used for smoothing concave curves.
PLATE or BISCUIT JOINER
A tools which cuts small slots in boards. Inserted into these slots are pieces of wood called biscuits. When glued and clamped, these can add strength to joints with gluing surfaces. Biscuits come in different sizes, but #10 (quite small) or #20 will work for most projects.
PALM and RANDOM ORBITAL SANDERS
These two sanders will save you a lot of time, though they have their limitations. A palm sander takes quarter-sheets of sandpaper and vibrates erratically. Sometimes this will result in little swirls in the surface of your piece. The random orbital sander takes special Velco-backed sandpaper. It spins and gyrates at the same time, creating a smoother surface.
For drilling straight holes and is much more accurate than hand-drilling. The bed height should be adjusted so that the bit, when up, is just above the workpiece. You can also adjust the speed for different materials (slower for metals and very hard woods, faster for softer materials). Be sure to clamp your piece well. If you don't and the bit catches it will fling the piece and can hit you quite hard.