I have decided to share my secrets on this, as a repayment for Culd's comic.  

First of all, if you play support, you generally don't want to get cs as it takes it away from the adc. Taking cs when your adc or other teammate isn't there is perfectly fine, but in general, high cs scores as support are a bad thing. XD

When you play a champion for a few games, you'll get used to their damage and how it changes with levels, items, etc.
Basically, you want to apply your knowledge of your starting damage and how it changes to cs.

For example, when I play Jayce (with my runes and masteries and a standard start of a health potion, flask, and ward), I deal about 78 damage at Level 1. So, when I see a minion at 78 HP or lower, I know I can get the last hit on it.
When I hit Level 2 (still, no new items), I deal 82 damage. So, when a minion is at 82 HP or less, I can get the last hit.
Remember that minions always damage enemy minions, so you may need to time your last hitting to account for that. For example, at level 1, I actually attack the minions when it has around 80 HP to give time for my attack to "finish". The delay in autoattack and damage changes depending on champion, so remember to account for that.

You generally don't want to autoattack the minions without last hitting as this:
A: Makes last hitting more difficult
B: Pushes your lane, making you more open to ganks
There are times where you WANT your lane pushed, but early game, you generally don't (an exception is when you want to recall or you notice your opponent recalled; pushing to their tower denies the enemy cs as the tower kills them all)

Depending on the champion, you can eventually clear an entire minion wave (getting the last hit on all of them) using your abilities. This can't be done at the start of the game (and you wouldn't want to anyway), but for example, by midgame I can clear an entire minion wave with Zed by using W > Q > E, then autoattacking the weak ones due to his passive. When you actually want to push your lane, it is important to know how to take advantage of your champion' wave clear.

Another example: When I play Twisted Fate, a red card on the middle melee minion followed by a Q will clear the entire wave other than siege minions (after you have enough AP and you level enough).

There are also a few ways to increase your cs other than the minions in lane. If you are bottom lane on blue side (the bottom left of the map), you can take golems if you are bottom lane. If you are mid lane, you have an easy access to wraiths and wolves. And if you are top lane on purple side (top right of the map), you have access to golems.
Taking these minions may not be worth it early game depending on the damage you take, but it does improve your cs scores. Just remember that it isn't worth it if you miss more minions in lane than you gain in jungle. I usually only take jungle minions if my lane is pushed to their tower and I can't gain much cs anyway.

Eventually you'll get completely used to the game and just know "okay, when the minion's health bar is at this point, I can last hit it with this champion" and looking at your damage and stuff won't be necessary. But, this will help to start out. xD

And a few other things...
1. Last hitting becomes easier if you press Escape in-game > More Options > Disable Auto Acquire Target. This will prevent your champion from automatically attacking things. Basically, you won't need to constantly move around to stop yourself from attacking and pushing the lane (though moving around is still good)
2. High CS scores are largely relative, so try to force your opponent to miss cs. Since you aren't last-hitting all the time (you have to wait for them to get low enough), try to harass your opponent while you wait. Then when you notice a minion get low, get the last hit, and repeat. Some champions are better at this than others, but there are some champions that completely deny their opponent cs with their harass (examples being Teemo or Yorick).
3. "Perfect" cs is considered 100 cs in 10 minutes. This will almost never happen, but try to have at least 80 by this point to start out. Then as you get better, increase your goal. 90 cs in 10 minutes is excellent. And this goal continues throughout the game - 100 cs in 10, 200 cs in 20, etc.
4. A kill is worth roughly 15 cs (and killing the same person decreases the value over and over, with the lowest value being only worth about 2 cs) So if your opponent is 10 cs ahead of you, but you have a kill, you are still technically ahead of them. Just remember that cs is a consistent way of increasing your gold - kills are a gamble.

And finally, if you jungle, you will usually have the second lowest cs in the game. Since you simply just clear your jungle for cs, the best advice I can give for this is to not waste too much time trying to force a gank. If you can tell a gank isn't going to happen, just go back, clear your jungle, and try to gank again / somewhere else.

I hope this helped  

Excellent explanation Those creeps won't know what's coming

I'm teaching myself InDesign and I made some infographics.