There is a definite art to plumbing with copper pipes. Thankfully it's fairly quick to learn, though your first few cuts and joins are likely to produce amateur results. If you've never installed copper pipes before, buy some extra parts and practice!
Most professional plumbers know that the quickest way to fit all the pipes is to cut them all to size and put them all in place, then go back and solder them all. This also lets you check that everything fits before you make the system permanent. However, if you're working in a tight space, you might want to fit and solder everything as you go. It doesn't really matter which method you use, as long as you're comfortable.
Measuring the pipe
Work from your starting point to the next fitting, one length at a time. You can measure the distance with a tape measure, by holding the pipe in place or, most likely, a combination of both. Mark the pipe clearly and don't forget to include the length inside the fitting.
Cutting the pipe
You can cut pipes with either a hacksaw (or reciprocating saw with a blade for cutting metal) or a pipe cutter . Manual saws are not recommended because they require a great deal more skill to use well and tend to leave a lot more burrs and imperfections on the cut edge. They also risk ends that are not square and use a lot more energy for each cut!
Pipe cutters are comparatively simple and accurate to use. Insert the pipe in the middle and tighten the screw until it bites into the pipe, then spin the cutter around a couple of times, leading with the wheel rather than the blade. Once the first cut is made, tighten the screw again and repeat, until the cut is complete.
Cleaning the pipe
Good joins need clean pipes. If you skimp on this stage and do not clean the pipes properly, you will get bad joins and inevitably leaks will follow. If you're cleaning a lot of pipes, you might want to invest in a wire brush that will fit on an electric drill, to save a bit of time and energy.
Remove any filings, burrs and imperfections on the cut edge and inside each length of pipe. The best option for this job is a deburring tool, though it can be done with a knife or the attachment on your pipe cutter.
Use a wire brush to clean the inside of each section of pipe and a grit cloth to clean the outside. If you don't have one of these tools, the other will work for both jobs. Make sure you remove all the oxidization to provide a clean surface for soldering.