For the initial construction you will only need the MDF pieces. Use a good quality PVA/Wood glue. You can paint the tower after you have constructed the MDF pieces if you wish. If you want to paint it before construction then make sure the tabs and slots are clear of paint.
Take one of the larger squares of MDF. Glue 4 of the smaller pieces into the slots as shown. Remember to add glue down the edges where the pieces join as well. The tabs will not sit flush with the bottom of the slot, they are purposely cut shorter.
Glue one of the smaller squares on top. Again, you will see that the tabs don’t fit flush.
Add 4 more of the small pieces of MDF into the same slots, this why they are not cut flush.
Add the next smaller square piece.
Add the last 4 small pieces.
Add the 4 larger rectangular pieces using glue on all areas that touch another piece.
Glue to 2nd larger square piece on to the top.
The greyboard pieces are used as shown but you can decorate these any way you wish before you attach them.