It depends on who you're playing. Some characters just need to play defensively early on. If you have a range, poke them with the range move/attack to keep them at low health, while staying as far away from them as possible. If your melee, it gets trickier. You generally only want to attack them as melee if you're tanky early on, or their health has already been whittled down by other forms of harass. All the while, remember to keep farming. Harassing won't do you any good if you aren't getting any gold while they are. The balance takes some getting used to, but they're all important skills to learn.
Just as an important skill to learn: learn to last hit. Autoattacking minions is usually a very bad idea. Remember that you only get gold if you kill them with the final hit. Continually attacking them will only push your lane towards their tower, where it gets tougher to deal with them and sets you up to be ganked by other champions. Unless you're a character with amazing range, it's very rarely a good idea to push someone to their tower. Learning to last hit while playing defensively is very important for a lot of champions.
Trust me. There are people at Level 30 who don't know how to last hit and it screws them over so much.
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Black Turtle did a pretty good job.