Connecting up to the strip is fairly easy, you'll want to solder four wires to the copper tabs. We'll use white for +12V, then red, green and blue wires for the corresponding LED colors.
Cut away the waterproof overmolding at one end of the strip. The strips are symmetric so it doesn't matter which end you use.
Scrape away the rubber to expose the copper pads.
Melt some solder onto the pads to tin them and also burn away any left over rubber.
Solder the four wires on. We used stranded wire, which is more flexible and is probably a better choice than solid-core.
To protect the wires and maintain some waterproofness, you can use heatshrink.