Learn Finnish: Sinä teit sen oikein.

The word for 'correctly' here is oikein. To make it comparative, we look at its base adjective oikea (correct). We add the comparative adverb suffix -mmin to the stem, which gives us oikeammin. So, 'You did it more correctly' would be Sinä teit sen oikeammin.

Why do we use sen (it) here instead of the partitive form sitä?

We use sen because the action of doing it was fully completed. The verb tehdä (to do) takes a total object when the action is finished, which means the object se (it) takes the form sen. If you were still in the middle of doing it, you would use the partitive sitä.

Teit comes from the verb tehdä (to do). Why does it look so different from the dictionary form?

Tehdä is an irregular verb. When we put it in the past tense, the stem becomes tei-. Then we just add the standard personal ending for 'you', which is -t, giving us teit.

I have also seen the word oikeasti. Could I use that here instead of oikein?

Not in this context. Oikein means 'correctly' or 'the right way'. Oikeasti means 'really' or 'truly' (as in, not joking or pretending). Using oikeasti here would change the meaning to 'You truly did it'.