You can order the EL wire pieces pre-soldered if your design is relatively simple, and you want to skip this step.
The sketch below illustrates the method I use to solder EL wire. If you'd like more detail, you can get directions from the places that sell EL wire, or see this instructable:http://www.instructables.com/id/How-to-Solder-EL-Electroluminescent-Wire/
For each piece of EL wire in your design, cut the proper length (with at least a few extra inches at each end), and solder the end of each piece to a connector, or to a double-conductor piece of ribbon cable that is long enough to reach the driver. The polarity does not matter - either wire can be connected to the center core or the outer wires. There are many methods for soldering EL wire, for any of these you should end up with a reinforced region with heat shrink tubing covering the junction.
I strongly recommend that you test the wire at this stage, joining the two conductors to an inverter, before it is attached to the garment. This is also a good time to join the pieces together to test the overall brightness, and decide whether you'd like to use a stronger inverter. You can achieve a higher level of brightness by overdriving the wire (e.g., attaching a short length of wire to one that is designed for a longer piece). It will burn out the phosphor on the wire faster, but that might not be important for some applications. Under normal usage, EL wire should have 3000 to 5000 hours of glowing life before the phosphor fades to 1/2 of its normal brightness.