How can we combine our observations of large scale structure...  ...with our models of structure formation... 
... to learn about the universe?
Example 1: Structure grows differently in different cosmological models. For example, in low Omega_{M} models, structure grows a little, then stops. In high Omega_{M} models, structure continually grows. Why?
Adding a cosmological constant also strengthens structure formation. Why? What about in the future?
Simulations of structure in the universe at the present time under different cosmologies 

Dark
Matter only models (no dark energy) 
Flat
universes with dark matter and dark energy 

Example 2: In Omega_{M}=1 universes, galaxy clusters are extremely rare in the high redshift Universe. Why? Remember, it takes time for clusters to grow. We know how many massive clusters there are currently. In low Omega_{M} universes, structure stops growing early, so there ought to be roughly the same number of massive clusters at higher redshift as now. On the other hand, in high Omega_{M} universes, structure is continually growing, so we should see fewer massive clusters at higher redshift.
from Borgani 2003
So here is a massive cluster at a redshift of z~1:
Current estimates of Omega_{M} from these
studies give
values of Omega_{M} ~ 0.3
or so....