This tutorial is made using UK terms (although I have indicated the US terms where applicable in brackets). I am right handed, but if you are left handed simply work in the opposite direction turning the work to best suit you.
Working the first two squares
While on the topic of granny squares, today I’d like to teach you a join as you go method for granny squares.
To start with I have made a complete granny square of 4 rounds. If you missed the tutorial on how to make a granny square you can access it here. This completed square is the one I will join the next granny to on its final round.

The next step is to make another square and complete it up to and including the third round. Ensure that you are in a corner to begin the joining process.

Now we will make the first half of the corner. To do this chain 3 (counts as first stitch), and then make 2 more treble crochets (US double). Then chain 1.

Now pull up a loop and remove your hook. Insert your hook into the top corner of the first granny square (coral) and make a slip stitch.
You will need to turn the squares as necessary while you work. It is important to always have the right side facing.
Next work 3 trebles into the corner of the second granny square corner, thus making a complete corner.

In other words you slip stitched into the coral colour square’s corner, and now you are completing the corner clusters on the purple square.

Now draw up a loop again and remove your hook. Insert your hook into the next open space on the first granny square (coral) from front to back and return the loop (purple) onto the hook.

Pull the loop through and make a slip stitch onto the first granny square, then make a cluster of 3 trebles (US doubles) into the next available space on the second granny square (purple).

Repeat the process of pulling up a loop, inserting your hook into the next available space on the first square (coral), from front to back, return the loop (purple) onto the hook, pull through and make a slip stitch onto the first square (coral). Next make a cluster of 3 trebles into the next available space on the second square (purple). Continue doing this until your reach the corner on the purple square.

At this point things might look a little off. It seems like the corners don’t line up. Please don’t panic. It’s all part of the plan. The next step is to once again pull up a loop and remove your hook from the loop. Next place your hook into the corner of the first square (coral), from front to back, and make a slip stitch. Now we are going to make the first half of the corner on the second square (purple) by making 3 trebles (US doubles) into the corner on the second square (purple). For now we are finished with the first square (coral).
Next chain 2 to make a corner and work another 3 trebles (US doubles) into the corner on the second square (purple). At this point it may feel a little off as the two corners don’t actually connect, but it is important that they are this way for when we join another square diagonally. This will be explained later on.

Now you will continue working around the second square (purple) in the normal manner and join with a slip stitch into the beginning cluster. Fasten off.
Your work should look like the image below. Don’t worry if it’s a bit wonky like mine. If you used cotton it’ll need blocking and the squares in the image have not been blocked yet. You can access a tutorial on blocking by clicking here.

Adding a third square
As with the second square (purple), you will begin another granny square and work it to completion of the third round.

Ensure that you are in the corner of the third square (vanilla). We will be working from right to left, joining from the bottom right of the second square (purple). If you are left handed you will work in the opposite direction.
In the top right corner of the third square (vanilla) chain 3 (counts as the first stitch), and make two more trebles (US doubles) in the same space, and then chain 1. You have made the first half of the corner.

Turn your work as needed. You will note my work is turned frequently.
Work the third square as you did the second square to the first, until you reach the corner. Once you have reached the next corner of the third square (vanilla) make the first half of the corner by working 3 trebles (US doubles) and then chain 1.

We are now going to join the third square’s corner diagonally to the first square’s corresponding corner. As indicated in the image above remove the loop from your hook, insert into the correct corner on the second square (coral). Pull the yarn through and make a slip stitch. Now complete the corner on the third square (vanilla) by making 3 trebles (US doubles) in the same corner you started in.

Now continue working around the third square (vanilla) in the normal manner until it is completed. Fasten off.

You will note that this join looks lies diagonally. You can experiment with how you insert your hook into the joining square, the number of chains you do before the cluster, and so on . All these factors will give a different looking join. The principles of joining, however, are the same, and remember to always join a corner on the diagonal to ensure a neat and symmetrical join.
Now for something a little different
As per the above, I’m going to show you how inserting the hook differently, and using chains, can change the look altogether.
To begin make a new granny square up to and including round 4. Do remember that you can join after any number of rounds, you just need to make sure that you start with one complete square, and join the rest on the final round.

Next make another square up to and including round 3. We will be joining on round 4.

You can turn your work as needed, but remember to always work right side facing.
Ensuring that you are working from the corner of the second square (in this case vanilla) chain 3 (counts as first stitch) and make 2 more trebles (US doubles) in the same corner. This will make the first half of the corner. Next chain 2. Pull up a loop and remove from hook, insert the hook into the first square (ruby pink) from back to front. You’ll note I’ve turned my work to make this easier. Return the loop to the hook and pull through. Now make 3 trebles into the same corner, thereby completing the corner, and chain 1.

Remove the loop from the hook, and into the next space on the first square (ruby pink) insert the hook from back to front, pull the yarn through and make a slip stitch. Now work 3 trebles (US doubles) into the same space completing the cluster for that space. Chain 1.

Repeat into the next chain space until you reach the corner. In the corner of the first square, pull the loop through and make a slip stitch. Now make 3 trebles (US doubles) into the corner on the second square (vanilla) and chain 2. Make 3 trebles (US doubles) in the same corner, completing the corner for the first square (vanilla).

Complete the rest of the second square (vanilla) as per normal.

Those corners may seem a bit odd but once you join other squares, on the diagonal as per previously, they will straighten up nicely.

This join is not quite as angled as the previous method. You can play around a great deal with where you put your hook and how many chains you use. That’s the awesome thing about crochet. You’re only limited by your imagination.
That’s it for today folks.