Hmm I've never installed after market lol. With any luck they should just connect to the old connector. If not I'm sure they would include something telling you which wire is power and which one is ground on the speaker it self. Then you would just have to find power and ground on the harness with a test light.
You don't really have to solder it if you don't know how, the next best thing would be to get some heat shrink connectors that you crimp then heat up.