To create your first linked stitch, you will work over the chains. There are two ways to do this. The first two stitches are the same for both  methods. However, you will need to know which method you want to use because one uses one more chain than the other.

For a triple crochet you normally yarn over twice, then insert hook into your stitch and pull up a loop. This gives you four loops on hook.

In the linked you will end up with four loops on your hook, but you will not get there in the traditional way.'

1) First you insert hook into the second chain from hook - using whichever method you choose. I am using the back hump. yo, pull through (2 loops on hook)

2) insert hook into next chain, yo, pull through, (3 loops on hk)

Here's where you have an option. You can skip the next chain (as I've done) and go into the fourth chain. OR you can not skip the chain and just into the third chain.

The reason I skip the chain is because I find it helps the stitch "stand up" so to speak. I saw this on Brianna's YouTube (Crochetside) and I adopted it.

If you prefer not to skip the chain, you can see a video demonstrating that method at  The Art of Crochet by Teresa.

Both methods work equally well and there is nothing wrong with either. Use whichever you prefer.

This is just a different view of the previous photo to show the back loop.

Here you see where I skipped a chain and inserted hook into the next chain, keeping all loops on the hook - just as you would in Tunisian crochet (Afghan stitch)

Now using the four loops you have on the hook, you will make a triple crochet. If you don't know how to make a triple crochet, you can see the tutorial on that.  (yo, pull through 2 lps) 3 times

Note that you can use the linked stitch process with a stitch of any height. To  make it larger just go into more chains and work them off 2 lps at a time until there are no more lps.

See those two horizontal loops on the stitch.  Those two loops will count as your "normal" yo twice for a triple crochet.

 

You will insert your hook under the 1st loop, yo and pull through.
 

Keeping that loop on the hook, insert hook under 2nd loop, yo and pull through (3 loops on hook).

Insert hook in next chain

yo and pull through (4 loops on hook)

Complete a triple crochet as normal, using the four loops on hook
 

continue working linked triple crochets as you did previously, using the two horizontal loops of present triple crochet and into the next chain.
 

here is a row of linked triple crochets

For the second row, if you want to do the skip a chain, you will chain 4. If you don't want to skip a chain, chain up 3.

Then work into the chain just as you did at the beginning
I did not do the skip a chain for this row, to show the difference

 

inserting hook into the first stitch of the row (do not skip a stitch as you do with regular triple crochet)

Two pictures of two rows of linked triple crochets