There are answers both complex and simple, really depending on your actual use case.
This simple answer is just to AJAX in a template that does what you want. There is no reason you can't have a template that looks like this:
accessed url: my_template_group/ajax_entry/100
Now if you need something that is more akin to an API for Channel Entries, you are looking at crafting your own plugin/module. I can't tell if you specifically want to select certain fields to return or just need something simple. If your use case is small, you could just have 5 or so special templates like the one above and just AJAX the template you need when you need it.