I have done a chain and worked some half trebles back along it (in the back ridge to make a tidy edge) and am now ready to work a dc (US sc) into the side of the dc that was made immediately before the chain.

Here I am getting ready to push the hook through the side of the dc.

Now I have pushed the hook through the side of the dc - under both strands.

Yarn over hook ready to pull a loop through the side of the dc.

Pulling the loop through the dc.

Loop is now pulled through the dc.

Yarn over hook getting ready to pull through two loops on hook.

Pulling through the two loops on the hook.

Completed dc.

I have now skipped 1dc on the base row and worked a dc in the next one. See how the appendage is neatly and securely attached? Your pattern will probably give variations on these instructions but the principle should be the same.