-The base plate itself is no different from a regular foundation, except that it has a smaller A1 or A2 bearing area (in the bearing stress formula). I think it might be A2, I can't remember off the top of my head.
-The concrete pier should be designed as a concrete column with axial load, and moment if there is any. Depends on your loading, but for most buildings up to 7 stories, nominal reinforcement of 1% should work.
-Concrete pier should have some nominal dowel reinforcement per ACI to tie it together. I just extend the same size bars as in the pier to make them dowels, but ACI allows for smaller dowels to be used.
-If your anchor bolts have uplift and/or shear, you need to check them for concrete breakout and a few other things with the correct edge distance. ACI has a section on anchor bolts. It's very tedious; you just run through it step by step. Or close your eyes like I do and use Hilti Profis to do it for you, though you should at least verify the results for one case.
-If there is uplift, I think the anchor bolts should have long enough development length to develop a tension splice with the concrete pier vertical rebar.
Hopefully I didn't miss anything, but that should cover it. The base plate and anchor bolt design is kind of like designing a connection to a small foundation.
