If you expect an early invade and are invading early yourselves also, you will likely need to place several wards at level 1 so that you have a very good idea of where the enemy team is. However, since the proper places for these wards are so situational I won't go into detail about that here and instead assume that you're doing a "standard" start with no invades.
These are basically all of the places you want to ward during laning. Obviously there are times that you need your own side lane bush warded, which I don't have pictured, and if there's ever a time when you feel the need to have sight somewhere else then put a ward there.
Keep in mind also that you don't want to be using too many wards during laning. If you're playing passively, you should be able to get away with having only two wards---one in a lane bush and one in tri on blue side or one in a lane bush and one in between tribush and the river bush on purple side. If you're playing aggressively and have control then you can leave out the one in their side lane bush, but then you need both river and tri warded, and if you push to their tower it's a good idea to put a ward that sees lane past their tower. Almost never should you have more than three wards at a time unless you're so far ahead that you can push past their first turret and lane at their second turret, in which case you're far enough ahead that the extra 75 gold doesn't hurt you that much.
Try to have a sense of where the enemy jungler and midlane are. If their jungler showed top 10 seconds ago, and their midlane just based with 10 hp, you don't need a tri ward right now. Wait another 10-20 seconds before warding it.
If you have a teleport on your mid/top, try to get a ward to the end of their bush right before the lane starts pushing back to you so that your teammate can teleport behind them if they extend. And if they have a teleport, anticipate this ward and buy an extra pink ward---it's worth it to permit you the security of pushing out and continuing to farm, even if you play somewhat passively due to the teleport.
Next time I'll talk about lane positioning; warding took longer than I expected it to, and I'm trying to keep the average length of posts on the shorter side.