When logged in to your account, you can find comics through a number of ways such as Search, New Comics, Browse, etc.
When browsing a list of comics, you can click the Collection icon to add it to your Collection. This is the second icon in the list of buttons underneath the comic cover. Alternatively, you can click the menu icon next to these icons to expand your options and add the comic there.
You can also click the comic cover to go to it's page. From there, you can click the Add button if the comic is released or click the faded Have It button.