Weaving is near useless and is really only good for keeping the clag off the tires, which we don't have in LFS. The best way is to alternate sliding the rear and the fronts in corners. Slide the rear with power, obviously, slide the fronts with sharp, exaggerated steering input to induce terminal understeer.
On straights, accelerate then brake hard.
If this was real life I'd tell you to take at least 2 laps of slow (7/10ths) running to acclimate the compound on a new set, but we don't have to worry about that in games. Just drive the balls off it till the screen is green.