To easily turn brown grass green, tap the grass button found on the photo edit screen:

Now brush over the grass that you want to turn green:

And you're done!

Optionally, you can use the color buttons and sliders to change the exact shade of the grass.

The "Auto Mask" switch controls if you want the brush to only affect similarly colored pixels. The default is on. This is useful to contain the green on the grass and not the sidewalk, etc.

If you do paint over something you don't want green, use the "Erase Grass" button to erase what you don't want included.

If needed, you can zoom in using two fingers, for more precise control.

Now you know everything there is to know about how to turn brown grass green. :)