How should I put my funding history in CV/cover letter?
This will vary greatly by field so look at examples of CVs in your field. In general, it is very common to list the title, the start/end dates, the agency, the amount and your role in the grant on your CV. In some fields, it's also acceptable to list unawarded grants (we all know that obtaining funding can be a bit of a gamble - so many departments like to see that you're trying). I've never heard of funding being listed in the cover letter - but, again, that may be something specific to your field.