This is really not as difficult as it might seem. All the puzzles are small (<100 pcs) and the only ones which are challenging at all are the ones which are timed or where you compete against bots. The last challenge is to assemble a puzzle which is a checkerboard and you'll have to be systematic to beat it.
1) Assemble the frame.
2) Arrange your pieces around the frame.
3) Look at the tabs/slots to find pieces that might fit. Look for color and whether they cut across one, two or four squares (i.e. are solid, have a line through them or have a cross in them).
4) Be systematic - if you randomly try pieces the last puzzle will take forever.