@ DavidB
It’s pretty straightforward. How much you need to do depends on what you’re going to use it for
Check out what size the existing joists are – 2×4 will need a fair bit of strengthening, 2×6 or bigger less so. Also, how far apart they are spaced as that makes a difference.
You can sister the joists – i.e. attach new joists to the old ones side-by-side. The new lengths should preferably sit on the end walls/bricks same as the old joists.
You could also attach the new joists on top to make the old ones taller.
I went with sistering to strengthen the old joists (not all of them needed it – it’s a mid-period Victorian terrace and the joists went from 2×4 in places to 4×8 in others)
The heights of the joists were all over the place, so I added another set of joists at 90 degrees and built these up or chiseled bits away (of the upper lengths, not the old joists!) so they sat as level as possible. I then boarded it out with T&G 18mm chipboard screwed to the new leveled joists.
Seems pretty solid, a little bit of bounce in places, but no ominous creaking. Probably not up to current building regs, but it’s only going to be me up here, not planning on having a party!