I would start off by looking in some books in the library and getting inspired about what you would like to achieve in the garden. Do you want to tend it and grow things, or do you want the minimum maintenance?
Then start to gather ideas together on paper. This could just be a list of things you want to have eventually. Perhaps a children's area (which can be cheaply put together with car boot sale finds). Perhaps a small area where you can grow flowers? Perhaps a lawn where you can sit in summer? A patio or decking area to eat outside? A couple of garden chairs? Again most of these things can be done gradually over years by buying from car boot sales etc.
Then draw out a picture of how it would look.
The point of all of this is that if you are aiming at something nicer it will motivate you to get it done. It is really hard work turning over a garden and having a clear picture of what you want to replace the mess with will make it easier.
Then make a plan of work and schedule it in for a few weekends. Start by tackling the bigger weeds like brambles. They may need to be dug out, but sometimes it is better to start with a weedkiller which will kill them of, leave it a couple of days, then dig them out. Reduces the chance of them coming back while you aren't looking.
Existing grass can sometimes be rehabilitated, as long as it isn't waterlogged or too compacted. You will need to dig out any big weeds, then spike lots of holes in the turf and add sand. Once you have done that, rake over the surface and remove any yellowy hay-like bits. Then sprinke some grass seed on the bare patches. If you are short of time and money, it might be easier to do this than start again.
You could buy some seeds at this time of year which will grow nicely and give you quick results. If it is a bright spot, you could sow a cornfield mix. That doesn't need good conditions or nutrients to grow and will give some results quickly for very little effort. Maybe clear a patch of soil and sow a tiny meadow at the back?
Post too long now, but if you get back to me with more details of what you like I could give more ideas....