Having been in your shoes 5-6 months ago, I would suggest doing this in order with one caveat. The end of the Season is almost over and there are some pretty big changes coming in terms of jungle, items and jungle/support gold. This is probably going to mean little to you right now, the basics of the game are going to be the same. So when you read guides/tutorials or watch videos just be aware some things will be different.
1) Pick a lane and a role. ADC, Support, Mid, Top, Jungle.
-- I suggest picking up support first as it will give you a more passive role to play. You don't have to worry about last hitting. It'll get your feet wet with the game, and you'll have more time to observe the ebb and flow of the gameplay because you're not concentrating as much on things.
-- Expand to other lanes and play some free champs, get a feel for the rest of the game and how it's played. Do this for the next 25 levels or so. The more you understand the map at large, the better you will become. The more map awareness and knowledge of mechanics the better you will be in the mid to late game.
2) Don't spend any IP on champs. Save all your IP for runes. You can buy T1 runes to fill out one or two basic pages. Then save everything for T3 runes at level 20.
3) If you don't mind spending 5-10 bux on the game every once in a while, buy champs as they go on sale. Don't pay full price unless you really don't care about spending an extra $10 on something.
4) Once you get comfortable with the game and you decide to play a specific lane for a while, go into a custom game against the AI and just practice last hitting with the champ you like. Get used to the animations and how much damage you can do. Last hitting is very important because it's the difference between a very very good player and a meh one. 10-30 cs difference is a huge power divider as you transition between phases. 30 cs is a kills worth of gold.
What I still do when I have internet access but can't play the game is watch videos of pro streamers. It's really the only video game I enjoy watching people play. Best channel in my opinion is the Miss Fortune and Miss Fortune RED channels. There's also ProFanBOI. Just type in a champ and watch gameplay. You'll be able to watch how people use their skills, their positions and gold/item flow throughout the game. Then play the champ a few times, and if you like them, go watch the videos again.
This game is really fun with friends. I hope you enjoy hit. Add me to your friends list if ya like "Mr Razorface"