Step 5: Prepare wire connections
First, make a chain of wires to connect all the (+) leads. Cut the wires in the lengths you will need, allowing at least 10-20% excess length (more slack may be needed for stretchy fabrics). Strip about 1/4" of the insulation away from each end of each wire and twist them together tightly in pairs, end to end in the order they will be joined to the lights. This step is easier if the spacing between all the lights is uniform. If your light spacing is variable, keep track of where the segments belong as you make them.
Pre-solder the twisted junctions, making a decent sized solder blob adhere to each twist. This step is much easier if you can clamp the twisted junction with a set of helping hands or similar device.
Make a second copy of this chain for the (-) leads.
As noted in the list of materials, it is strongly recommended that you use stranded insulated wire. Solid-core wire does not withstand repeated flexing very well, regardless of wire thickness. If you use non-insulated wire or conductive thread, you will risk short-circuits when the wires move and touch each other.