Two Tips for Small Garden Design
Here are the two major suggestions that should get you started in the right direction.
Garden Up
The first rule of landscaping in small spaces is to make full use of every square inch of space and this includes gardening upwards - making use of all the vertical space you can reach.
Plan on gardening on house walls, fences and even creating structures in the garden allowing plants to grow up.
For example, if you want a sitting area, consider building a pergola over top of it where you can grow climbing roses up the posts (in the sunshine areas) and flowering vines such as Wisteria up the poles to grow over top of the pergola (prune off all wisteria branches on the poles to allow the roses to dominate there)
Do you entertain and cook outdoors? Then create a maximum space there for doing that kind of thing

This was a small garden 20'x 20' I built (this is a first year garden) to hold all my plant acquisitions and plant trials. So many things were in containers, the grass was eliminated, paving stones led me to my car and everything else (including some water garden plants) was a garden or a container garden.
Garden Fully But Limit Yourself
Small garden design spaces demand maximum use of space. This means you identify the most important things you want to do in your garden. Do you want to entertain? Do you want to cut grass? Do you want to grow a vegetable garden? Do you have dogs that share the space?
What are the three most important things you want to do in the garden?
Design for these three things (or fewer but never more) A small garden isn't normally good at being all things to all people so pick what you truly think is important (note if that changes so can your garden design - these things aren't carved in stone).
This means if you want to have a vegetable and herb garden, then you allot space for this - and your vertical spaces are designed to grow fruiting trees on espalier systems to make full use of fences and walls. You create great container gardens to make maximum use of space.
Design for your main uses - not what others think you should have. I note the biggest thing most folks have trouble eliminating is the lawn. They "think" they should have a lawn. You don't need a lawn; particularly if that lawn-area is partially shaded. Get rid of it and put areas in there you will use. This, after all, is your small garden design for your own use - not for anybody else.

The Japanese garden tradition is superb for creating garden-metaphors - making each piece of the garden stand for something else - rocks for mountains, small ponds for oceans.
