How do I find out what my competitors rank for?

You can get most of the way without paying for a tool:

• Search your own core terms and note who appears repeatedly - those are your real search competitors, which may not be your real business competitors.
• Read their page titles and headings - the terms they are targeting are stated there.
• Check what they answer that you do not - the gaps are usually questions, not keywords.

Paid tools speed this up, but the judgement about which gaps are worth filling is yours either way.