You don't mention whether you prefer studying chess with books or at the computer, so I'll toss a couple of ideas at you for both.
Books
Russia Chess House has some good beginning tactics books (Chess School 1a and 1b) with a thousand or so basic positions, showing some elementary checkmates and basic tactics. They make a pretty good starting out resource, if you can find them. Then there's C.J.S. Purdy's Guide To Good Chess which can help fill in the instruction gaps (the Chess School books have no text, just positions to solve).
Computer
I haven't seen CT-Art For Beginners, but everything I've seen about CT-Art tells me it's probably good. There's a couple of other basic tactic trainers out there to work with as well, for example Chess Tactics For Beginners. I like that series (Originally from Convekta, most of the time these days I see them coming from Chess King) because they run in several modes (a Learning mode that is typically divided into "Theory" and "Practice" and a "Testing" mode where they give you pretty much nothing except the position and who is to move) so you can work through the app on different levels of detail; as your strength improves, you can move up, or drop back down if you need some extra help in certain areas. On iOS, at least, the app itself is free, and it has 10%-20% of the positions in it unlocked. Once you decide this works for you, you can unlock the entire app for typically $5-10.
Play against other players, and try to play against folks a little better than you. (Most humans don't have the patience to play a lot and never win, so it helps if they're just a little better than you, not grandmaster level.
As your skill progresses you can move up to harder tactical puzzle books or to CT-Art (the main app can find hard enough puzzles to make a master sweat). Keep track of how you're losing games. Do you overlook opponent's tactical chances? Work a little more on tactics. Are you confused about what to do in certain positions? Look in online databases for other games in those positions and see what others have played.
One bit of advice I got a long time ago was to pick two players, one from the past and one playing today, and simply play through a few games of theirs every day. When you start out, don't spend a lot of time analysing them. Just play through them like a watching a movie. Eventually you'll notice you are thinking a little about the positions. What you're doing there is essentially loading your brain with chess patterns played by those grandmasters; creating "landmarks" in unfamiliar territory that your brain will start to use to find its way through it.
Revisit those games as you improve, and this time you'll be thinking a little more about the positions, because your brain has already started to connect the patterns together. Each time you revisit them, dig a little deeper into them, as you improve you'll be better able to spot the why's of a move. That approach helps keep you from being discouraged. Back when I was a novice, I didn't know how to begin analysing a GM game; had no idea what was going on. But as I played over more and more games, I started to connect the ideas, and I could start reasoning. First it was "this is a typical move in this position" and then it became "this move keeps white from occupying an outpost" and so on. By not demanding too much at the start, it was easier for me to stay interested.
Certain ideas and positions will catch your fancy; don't be afraid to depart from your planned study and follow them. They're indicators of the kind of chess you like to play, the beginning shape of your own style. Just as no one plays like Nakamura except Nakamura, no one will play like you, except you. Follow and see where it leads you.