You could use many ways by culturing cells in non-adherent culture dish or low nutrients conditions or by drugs to promote spheroid (cell aggregates) formation. This spheroids can be cultured in the same dish, leading to connecting among the spheroids, eventually becoming organoids.
I agree with Sang. However another way to do it, is to suspend detached cells in hanging drops. This way, your cells will form spheroids too. The advantage of this method is its easiness if you want to test your cells.
There are many ways how to make 3D cultures. We use several of them:
1) 3D Bioprinting (http://www.n3dbio.com/products/magnetic-3d-bioprinting/) - it is very easy to make spheroids by this method and you can make them in 1-2 days from even different cell lines mixed together.
2) 3D Microtissue - its is quite cheap method and you can make many spheroids in the same size at the same time.
3) Hanging drop technique - it is very cheap and easy method, but the problem could be that sometimes spheroids do not form, thay are as loose aggregates;
4) Growing spheroids in ultra-low attachment plate - usually we had the same problems as with hanging drop technique.