Twitter lets me see posts of the last 2-3 days in my timeline. How can I read older posts?

[Michael]

I assume you mean you're trying to see all of the tweets from people you follow. If that's the case, you can select the person and then at the bottom of their initial page, click "More" until you get your fill.

In the future, you could think about using something like TuneIn.com, which saves your past information and actually helps to surface the best stuff in the big mess of people you follow. Check it out.