Best way to get IP?

Farm bot games.

Buy an IP boost, lol (you can get a free one here, if you haven't already gotten it)

I would usually just play 1 game a day, bots, for first win bonus. It's probably the most time efficient way, since you're guaranteed a win, and can probably end in like, 15 minutes if you're really efficient about it.

Grab a party of five and do some bot games.

Depending on how much you're willing to invest into it. A party bonus of 5 is like 400% regular IP gain. The IP bonuses in the store stack, so you can buy a 10-win boost and a 1-day boost if you wished.

Other than those, IP earned scales with the amount of time in a game. It really doesn't matter as long as you're playing the game. Bots have the lowest amount earned. Blind second lowest, and I think draft/ranked are equal (not sure.)

The best way is to play 1 game every day for the daily IP bonus.

The fastest way is to spent real money. But why would you spent money on something you can already get for free?