How it works
This is the side panel you will see when you are logged on. Most of the links are self-explanatory, but there are a few points to make.
The (num new) after Browse comic list are visible when new comics have been added to the database since your last visit.
The (num new in anothernum) is a quick summary of how many comics there remain to be read in your subscriptions in total and in how many comics. This number will change when comics get new pages and when you read them.
"Your account" has options controlling the layout of the site and account details like your email address and password.
This is what comic listings generally look like. The comics you have subscribed to have been marked with and the unsubscribed ones have next to them. New additions have (new) in front of them. The names themselves are links to the comics' info pages.
The "Bookmark the first comic" checkbox controls whether your bookmark is set to the first or the last comic page when you subscribe to comics. Bookmarking the first page is what you usually want to do if you haven't read a comic before and want to start from the beginning.
Checking for updates
This page is where the meat of Piperka's functionality lies. In fact, http://piperka.net/updates.html may be the page you want to set your bookmark to from your browser.
"Set bookmark" takes an URL from a comic's archive pages, finds the corresponding comic and the page the URL refers to and sets your bookmark to the next comic from there. If you were not previously subscribed to the comic, it also adds it to your subscriptions.
You can use this bookmark when on a comic's archive page to directly set the bookmark on Piperka and skip copying and pasting the URL on the updates.html page.
If the "Set bookmark here" checkbox is checked, the bookmark is set at the exact URL you have given. Otherwise it will set the bookmark to the comic page following the URL you have given, i.e. you won't see the page you have already seen twice.
"Revert updates" is there to undo the changes Piperka does to your bookmarks on redirects. You'll find a list of recent redirects you have used, following the links there will set your bookmark to where it was before the redirect. The net is an inherently unreliable medium and Piperka has no way of knowing whether you actually reach the comics.
Finally, there's the list of updates. By default, the links here serve two purposes. Firstly, it will redirect your browser to the page where you left off in the comic's archive. If it says there, e.g., (3 new) it will redirect you to the third latest comic page. And secondly, it will update your bookmark for that comic to point at the latest comic page. You may want to return here to use "Set bookmark" to set the bookmark to some other position if you didn't read the archives that far yet.
You can turn that second part of Piperka's functionality off on your account settings page. That mode also adds buttons to move your bookmark to the newest page without redirecting you from the updates page.