How on earth does this work? what do all the little numbers actually mean? I just dont understand it

The grade 6 theory textbooks are a good introduction to figured basses.

In short, it tells you which intervals to play above the given bass note. Starting with root, 1st and 2nd inversion chords the symbols are:

5
3

6
3

and

6
4

However, in practise, these are abbreviated to nothing, 6 and 6/4 respectively.

A few examples, in C major:
An E in the bass with 6 above it means play E, G and C.
A D in the bass with nothing above it means play D, F and A
A G in the bass with 6 4 above it means play G, C and E.

There are more numbers for 7th chords and their inversions, and a whole bunch of other things. In practise, unless you plan to take any harpsichord exams, you don't really need to know how to do it - from what I can tell it's all but optional on grade 6 theory.

Still, it's an interesting concept. I've always wondered how they work!

It's a great example of what my maths teacher used to call the 'principle of conservation of ink': write a whole chord in one note, optionally with a number or two.

Haha, I like that one!

The numbers refer to the intervals above the lowest note of the chord.

Figured bass gives you the least amount of information possible in order to give you the freedom to make your accompaniment fit the style demanded by the performance of the work in question.

A note with no numbers above it is a simple triad in root position, with notes a 3rd and a 5th above the bass (which is the note written). 3rds and 5ths are "obvious", so to speak, so they're never written down unless they tell you something particularly important (i.e. in 7th chords).

When a "6" appears with the note, the rest of the chord lies a 3rd and a 6th above the written note. Otherwise known as a first inversion chord.

"6
4" follows the same pattern, the rest of the chord is a 4th and a 6th above the written note - your second inversion chords.

7th chords are fun! There are too many numbers usually so reading them would be cumbersome - instead they just tell you where the root of the chord and the 7th of the chord are.

"7" -root

"6
5" -1st inv.

"4
3" -2nd inv.

"2" -3rd inv.

(very easy to remember!)