As promised here is the tutorial for the technique I use to join squares.
I've experimented several techniques, but this one seems to be the easier for me and I like the way you can't see the yarn you used to join the squares.
1. Choose the squares you want to join. If the squares need to be in a specific order, like in the Periodic Table Blanket, remember to start with the squares from the right.
2. Fold the top square over the bottom square.
3. Make a slipknot on your hook. Here I'm using a yarn with a contrasting color for clearness purposes, but it's best if you use a matching color.
4. To join the squares we are only going to work in the outside loops: the back loop from the square in the back and the front loop from the square in the front (marked in orange).
5. With the hook grab the loops as explained in the previous step.
6. Work a slip stitch.
7. Continue to slip stitch all the way across the squares and keep adding more pairs of squares to the left of the piece until you have all the squares you need. Make all the horizontal joins first and then all the vertical joins.
If you are making a big piece, like a blanket or a pillow cover, its best to have all your squares aligned first in the order you want to join them in. After joining the the first and second row of squares together, join the third row to the bottom of the second row and so on until you have all the rows you need.
In order to make the vertical joins turn the piece 90º and join using the same technique.
Hope you give it a try! If you have any doubts please leave a comment and I'll do my best to help!
Have a great weekend!