For people who look at pictures of optimal warding spots and give up trying to remember it, don't worry.
Here's a simple guide:
While Laning:
1. Make sure at least one rune spot is warded (whichever is closer to you). You don't need to ward both and it's a bit of a waste unless you have unlimited wards for some reason and you want to make love to your mid lane.
2. Use your remaining ward to cover areas where an enemy will gank you from. So this means the other entry to your lane that isn't seen by the river ward. If you can use this to also block a creep spawn, good. If not, don't worry about it.
3. Is the enemy going to pull creep camps? Ward it. If not, don't bother.
4. Refresh these as needed while laning continues.
After laning:
1. Assess your situation. Are you down towers? Is your team on the losing end? Generally, if you lost your towers you want to use wards to defend your jungle. This also applies if the enemy loves entering it for some reason (they're all gankers or they're roaming as 5). What this means is put wards at the two river entrances into your jungle. Then if you can afford it, put one in your jungle itself so you can see inside.
2. Is your team really aggressive? Are you tower diving and jumping into fights and winning a lot. Are you roaming a lot. Then ward their jungle and the back of their towers. Keep note that due to the nature of wards, whereever you ward in this case will be the location your team will attack. It's just a psychological thing, so you can influence your team's offensive behaviour like this. To repeat: Ward whatever you want your team to attack.
Base defense / Base sieging:
1. Not particularly vital at lower levels of play, but if you have nothing to do with your wards at this point you can basically just put them at the black spots of vision around your base. It helps a bit, but is definitely more useful for the offense since it'll help you judge when to jump in.
That's about it. If you want to counterward, just counterward all those locations.