(working off the assumption that you are playing as support)
My advice would be to watch your own minions. You probably shouldn't be farming much (except for
), so you can focus all your energy on watching the other laners, and the minions. If you do this, you can probably predict which of your minions will be the enemy's next target. If you do this, you can start to engage the enemy AS he goes to farm, rather than AFTER he takes the cs. This forces the dude to either use his first auto on the minion (and probably take some damage from you) or use his auto on you (and thus miss that farm). You have thus won the trade, and should leave before the other support/adc gets in your face.
Also, you don't have to engage all the time. I'm not sure what you play, or how, but some champions are designed around all-inning, rather than harass:
This dude is about all-inning, sure, but he is ready to all-in every time his hook is up
This guy doesn't harrass, or all in, unless his adc goes in. He is purely defensive, and is almost an anti-all-in support
This girl is all about harrass. Just slap them with your Q when they go to farm, and then leave. Your autos are literally worthless, don't bother trading with them.
See Soraka
I haven't really played her, but I think she is like Blitz. However, she requires more skill cause she is the one flying across the map, instead of pulling people to her. If she goes in at the wrong time (aka when the adc is in farmville), she will be punished
See Leona
AP supports: I know some people get triggered when they see this, but they are mostly geared towards constant harrass, finalizing in either pushing the enemy out of lane with backing, or an all-in in which the ADC (hopefully) gets the kill. Also, it isn't the champion that a support plays that determines a support, but the mindset. If your mindset is to solo carry the game, you are no support, even if you are playing soraka. If your mindset is to assist your teamates in both killing and not dying, then you are a true support, even if you are playing Illaoi.