The basics on carp are: ye can flip pieces by right-clickin, try not to misplace .... and as ye get used to the puzzles and pieces, ye'll be able to know which pieces ye need to finish a hole. Once yer down to 2-3 ye need, and ye know which they are, delay fillin that hole as long as possible to give ye more time to get those pieces. So let it shimmy and shake.
I always try to finish two adjacent holes, rather than try to fill them all simultaneously. That way you get two new holes for when the bigger peices come out in the rotation.