egen allows you to use some function such as "group", "mean", etc. Take a look at "help egen" to see all the function for egen. Some of them are very useful, especially when you use it together with "by".
You can save your database using "save *.dta" or store results with "est sto".
Finally if you want to see the various tests in Stata, take a look at postestimation commands (such as "reg postestimation").