The different types of champions require a different playstyle. In general you want to avoid jumping head first into a team fight and unleashing everything you can while hoping you won't die.
Tanks are meant to be meat shields with good CC, initiating teamfights so that the enemy team focuses on them, while your team attacks the enemy while they are busy. Carries and casters in general play more defensively and stay behind the tank. Positioning is crucial to the role you are playing in your team.
There are times to be aggressive and times to be defensive. At its core, LoL is a team game, and one person cannot win the game for everyone. The website provides descriptions of the various champions and their type so you can understand the role they fulfill. If you build a champion in a manner that does not synchronize with their abilities, then you are not using it to its full potential.
To get a better idea of how the game is played, you should look for beginner guides on youtube or watch some livestreams (you can find these under General Discussion) to see how games are played well.
Essentially there are three stages in the game: early, mid and late. Early game is when you go to lanes and last hit minions to farm for gold to buy items. Mid game is when people stop laning and start ganking and/or pushing. This often happens when mid lane hits level 6 or so, when they get their ultimates and use their level advantage to gank a side lane. Late game is when majority or all of the players have hit the level 18 cap and are still fighting it out.
During early game, you want to try and get champion and tower kills, while farming effectively at the same time. The better you farm during early game, the better advantage you have during mid game. If you are having trouble, play defensively and try to keep your tower alive while making sure you do not lose out in EXP. Some gold loss is reasonable if you are forced to "tower hug," but you want to try and keep your tower up as long as possible while trying to take down the enemy's tower.
By mid game, it's not unusual to have at least a tower down. The earlier you knock down a tower in your lane, the earlier you can move to support your teammates in other lanes to knock down more towers. While kills are important, you also have to remember that knocking down buildings wins games.
Late game is often when one or both sides has lost a number of inhibitors, and things are getting pretty intense, trying to find a good decision between defending and attacking. By this time, most would be some what close to finishing their item build.
There is a lot more to cover about the details about the game, and I can understand your frustration as I felt the same way when I first learned how to play DotA about a year ago. I was lucky to have friends who were willing to spend hours running me through the basics of the game until I fully understood it. I know there are good players who may be willing to coach you, as mentioned in previous posts, and you should take up the offer.
Once practice games are out again, it will help give you a better idea of how to play. As some have mentioned, it is hard to help and play effectively at the same time during a game as things are constantly happening. The game has a somewhat steep learning curve to understanding the basics, but once you get it, things should go a lot smoother.