I don’t really think you can do great deal to improve your social connections with people, particularly if you are an adult who already has a developed personality and character.
I was listening in accidentally to some couples talk. Some of them sound like that had each others rapport. Others however were just very pointless, meaningless conversations. The fact is, you shouldn’t need to hone your social skills with someone. If you had a connection with him/her, your conversations would just flow. In the case of dating, the mutual attraction alone would make conversations arise. It wouldn’t need to be forced. It wouldn’t even be awkward if either of you remained silent. The awkwardness only comes if the effort came solely from one direction. If you find you can’t build a completely conversation with someone, you should probably stop trying and move on. Clearly you have no connection or anything in common!