There are a lot of different ways to assemble squares together using a join-as-you-go method. Most will add a round to your square as you join one to the other.
The continuous jayg has become very popular because unless you have a knot in your yarn or some other yarn issue where you have to cut out a piece, you will have only your beginning and ending tails to sew in when you are done. This is a great time saver. I did not think this method was very sturdy until I made an afghan using the method for my son. I asked him how it is holding up and he had no complaints. He said it hasn't fallen apart and there are no holes in it that need repairing. It was made in 2008 so it is currently 4 years old and has been washed many times.
If you are an experienced crocheter, then you may be able to look at the chart and go from there. Once you have worked the method once, you will understand how it flows and will not have to spend time with the videos. If you are a beginner and have never worked a jayg, you may want to take the time to go through them. The total video time is about 40 minutes but you will likely have to stop a few times while viewing.
You might find it easier to work this method the first time if you actually number your squares so you can follow along with the tutorial more easily.
I am using granny squares to demonstrate this method, but you can use this procedure for any type of square. My granny pattern is (shell, ch 1) for sides and (shell, ch 3, shell) for corners. Note: With the granny pattern, the method works best if you work a complete left top corner on square #1.
Here is how we are going to be working it. Follow the arrows. Note that the arrows are ONLY to show you the direction in which you are going to travel. Your stitches will of course be next to one another, not with the space between the rows as the picture. You will always be working on the RIGHT or FRONT side of your square.
Right-handed chart below
Left-handed chart below
Here’s a video demonstration of the technique, in four parts.