There is a little message box at the bottom of the webpage on each trade. Just type in what you're offering and hit enter. Each message also gets it's own reply box, so make sure to use the large one at the bottom for a new offer.

Thanks! I was confused. I thought there was a button or something

There should be an orange "Let's Go" button for submitting a main offer for a trade or for saying "added", etc. if you agree to their main offer. For sub-replies (like if they agree or counter your offer), there is no submit button, you just hit Enter key.

Note that you should not hijack trades (don't make an offer to someone the trader rejected), add your own New trade instead.