The previous owner of the house neglected the garden for quite a few years because of health, so the garden was a disaster when I bought the house.
I kiilled all the weeds and bought some plants. The problem is the soil
has not nutrition. I don't want to use chemical fertilizer. Any suggestion
on how I can improve the quality of the soil?

Well, the usual preparation for gardens includes tilling, adding new top soil and mulching. Depending on the type of soil you have locally and the kind of plant you want, you can further improve soil's PH value. Have you tested your soil yet? Sometimes a weedy garden doesn't mean the soil is bad. Most likely, you can much improve your garden by covering the very basics: drainage, top soil, and mulch, last but not least, water often in summer.

Ok. I tilled and added some mulch, but forgot the top soil. The problem is not top soil because the soil on the surface is quite good from the mulchs of the past. When I digged a little deeper, I can see sand! Do you guys make your own compost?

Is sand a problem? That pretty much depends on what you are going to plant.
You can make your own compost but it is not expensive to buy compost from stores either.

You have sand underneath of entire garden? Is it common in your neighbourhood? We use to have a lot rocks in the garden, what we did was simply plant around it. Few people in our development actually hired landscaper to redo the entire beds. It all depends on time efforts, cost, and your goal. You can try plant some shallow-rooted perennials.

Never tried makingcompost myself though.