Welding exhaust tubing can save you a lot of money. It can be done with either a stick welder or a MIG wire feed welder, which is the industry standard. Weld the exhaust tubing away from the vehicle, if possible, to avoid fuels, oils and other flammables.
Cut the exhaust tubing to fit. The better you cut each piece, the cleaner they will fit and weld together. A reciprocating saw or chop saw will ensure nice, straight cuts that can be mated up well before welding. Use a grinder to remove any burrs or imperfections so that the seam is as gap-free as you can get it. This applies to the ends of mufflers or catalytic converters as well. Cut carefully so that the system mates up well.
Clamp the tubing together. The best way to ensure a clean weld and a good fit is to use c-clamps made for welding projects. Mate the pipes up as they will look when under the vehicle, and clamp them together so that both your hands are free for the welding process. Remember to make sure they are clamped well, because a weld is difficult to undo.
Spot weld the exhaust tubing. Because welding creates so much heat, spot weld the tubing together at three or four places first. Doing this will prevent the tubing from warping and creating hard-to-fill gaps in the steel. Simply weld small sections of the pipe for two or three seconds around the circumference and keep an eye on the opposite side of the tubing. If gaps occur, you can bend it into place easily for welding the other side, as long as only spot welds are holding them together.
Fill in the gaps with weld. Now that the tubing is spot welded and fitting up together nicely, you can go ahead and weld all the bare areas. You can weld right over the spot welds, too. Try to get a 100% weld all around the circumference of the steel so that there are no exhaust leaks once the system is put into use.