I've had a few questions about changing colors in Tunisian crochet and since I'm not the greatest at explaining things I decided to make a little picture tutorial...I hope this helps everyone!!
Begin your crochet as usual and pull up a loop. I have done three stitches in my first row and am starting my fourth stitch here:

Pull the yarn through and you now have another stitch (I now have 4):

When you're ready to change your color, insert your hook into the next stitch and instead of pulling up a loop in the same yarn, grab your new color

And pull it through:

There are now 4 loops of one color and 1 new color loop (5 total) on the hook.
Again, insert your hook and pull up a loop in the new color:

Now there are 6 total loops, 4 in the old color and two in the new color:

Continue your stitches until you are ready to change color again (if you choose, if not just finish the row) Once you're ready to change color again repeat the process again of inserting the hook, pulling up a loop in the new color:

New color loop on the hook

Finish your row to the end and begin your return row. When you reach your color change you will have one loop of each color on the hook.

Draw the color you are changing to through both of the loops

Work until you need to change again and repeat the process--one loop of each color is on the hook, pickup color you are changing to and pull through the loops

I found that when I change color in the row I get this hole between the two colors on the return row

To close it all you need to do is take the previous color yarn and pull it, but not too tight

On the back you are going to need bobbins if you want to carry your colors up through the work.

It really depends on what you're working on whether you will want to carry your colors through or if you'll want to cut them and weave them in.
Your row is finished

I really hope this helped you all with questions or anyone wanting to know how this works. This may not be perfect and it is definitely not the only way I'm sure to do it but its what works for me. If you have more questions just let me know!!
PS: Sorry I did thumbnails but I didn't want to make the post like extremely long.