A lot more information is needed, such as the size of your garden, what sort of soil you have and the aspect (eg south/north facing)
I suspect that, unless you have a garden big enough to support full sized trees, your best bet is going to be an awning of some sort rather than planting.

Most councils have a height limit for hedges between neighbours so ring them to ask what it is in your area. its usually about 8 feet which might not be high enough for you.

I agree with Urbanite - if you're overlooked from upstairs, the only answer plant wise is a tree, BUT you can't plant a tree with a good sized canopy close to a structure, house, wall, whatever, so that would appear not to be an option. Unless you want privacy 30 feet away from the house, as a minimum... so some kind of awning would seem to be the best option, otherwise its a pergola with climbers over the top.

Don't know the view the neighbor has of your garden but if is a good view, anything that you plant or construct and grow on may possibly cut your sunlight down so much the only thing that will thrive in your garden are shade plants and forget about relaxing in a chair to take in the sun....there won't be much to do that. My solution....when you go out into your garden, try not to think about your upstairs neighbor.

Or... don't do anything in your garden that you would rather your neighbour didn't see!

If conditions and circumstance allow...

Budlia:
many varieties, butterflies love them, quick growing, fragrant flowers, attractive looking, can provide a reasonable screen.

I hope this helps with your question ^_-