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I'm quite a reserved person too and have spent quite a lot of time trapped in awkward silences, particularly in my teens. I had quite low confidence, though, and as it grew, I found that conversation prompts would just pop into my mind without me really thinking about it. I believe I was just a bit too afraid of saying something daft in the past that I just froze up. Now that I no longer give a shit, I'll say (almost) anything that comes into my mind.
The thing that most helped me engage and build rapport with people better was some very simple advice I was once given - just ask people questions. Just about everyone's favourite subject is themselves, so just ask them something, let them answer, then ask them something else off the back of that, and so on. People will talk to you FOREVER about themselves and go away thinking you're amazing, despite all you really did was prompt them to talk about their life.
If you're confidence is fine, and you really just can't think of stuff to say, I'd suggest practising on soft targets. Go sit near and old person at a bus stop or park bench - they will talk the ears off you and will probably not even really care what you say to them as long as they get to talk - this is probably a good thing to do in general anyway as a lot of these old folks are just plain lonely, but it'll certainly allow you to practice.
If all else fails, just talk about the weather?