There are various ways of joining granny squares and other motifs together but here are a few of my favorite techniques. First of all you need to determine which technique is best for the effect you want and what type of motif you are putting together.

For granny squares and square motifs put together with a solid seam I use the following technique.

Lacing Technqiue

This one is my absolute favorite.
This one produces a flat seem that is hardly visible when you use the same color yarn as the last round in each motif.

What I do is when I finish each square, I leave an 18" length of yarn at the end and I do not weave it in. I use it to lace the squares together. I do weave in the starting end that is at the center of each square.

To start lacing with the 18" length, first put two squares together back sides facing each other so the knot of the 18" length is to your right and facing you. The length of lacing yarn on the other square should be on the bottom right, away from you. See Fig1. The way to stitch is first insert your needle into the back sqare from the inside to the outside in both loops. Then bring the needle through the front square from the inside to the outside toward you through the next stitch on the square going through both loops on square. Repeat this technique across the square to the other corner. When you reach the other corner, pick up another square and put together back sides facing each other and make sure the end of the yarn on the new square is right at the top right hand corner right next to your yarn you have threaded on the needle. You will work with this later. But keep it out of the way for now and continue stitching in the same manner across the side of the square where you are at.

To continue stitching the squares together, refer to Fig. 2 to see in what direction the stitches should go to.

Fig. 1: This is how to place the two squares together back sides facing each other.

Fig. 2: This is how to arrange the squares to be able to stitch them together in all the same direction.

Other Methods

Overcast Stitch:

With pieces together, wrong sides facing or laying flat right side up side by side. Pass yarn or thread through all four loops on edges of piece. Going from right to left always. Or from left to right if left handed.

Whip Stitch

Sew the two pieces together in the same way as the overcast stitch but work through the back lps only.

Crochet techniques:

With most crochet methods when joining you end up with a ridge. This is fine if this is the effect you are after. The one method that I do use which produces the smallest ridge is to place them together wrong sides together and slst them together through the inside loops only. that would be the back loop on the square facing you and the front loop on the square away from you.