The Hacker101 CTF is split into separate levels, each of which containing some number of flags. You can play through the levels in any order you want; more than anything else, the goal is to learn and have fun doing it.
Once you enter a level, you're going to be searching for the flags, using every skill and tool in your arsenal. Flags are placed in various locations -- they might be in a file, in the database, stuck into source code, or otherwise -- and your goal is to hunt them all down. Each flag looks something like ^FLAG^37ae568362f974017fa575f08cd215044cd6bb395c3f5e5e293ee5324ba6769c$FLAG$, so you'll know the instant you see one.
If you get stuck, try going through a level from scratch and see if you missed something along the way. Did you inspect every page thoroughly? Press every button? Manipulate every input? Try not to overthink it too much; the flags are usually more obvious than you might think.
If you think you've looked over everything, check out the hints for the level. Click the "Hints" link next to the "Go" button that launches an instance and you'll get a helping hand.
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Whether you're brand new or a seasoned hacker, you may also want to check out our companion site, Hacker101, where you can learn everything from absolute beginner to advanced hacking techniques. No flag on this site will require skills you can't learn from Hacker101.