DOC: improve groupby reference docs
An overview of the reference doc on groupby is given here: http://pandas.pydata.org/pandas-docs/dev/api.html#groupby (apart from the extensive user guide: http://pandas.pydata.org/pandas-docs/dev/groupby.html)

There are some things that could use some improvement:
- [x] add some missing functions to the overview in api.rst (#8231)
  - GroupBy.filter
  - `first`/`last`/`nth`
  - `count`, `cumcount`, ..
  - `name`: not sure what the purpose of this is
- [ ] add the `GroupBy` object itself to the api docs (and so automatically all its methods) (#19302)
- [x] put all relevant docstrings in the GroupBy class, and not only in the subclasses DataFrameGroupBy, SeriesGroupBy (eg now the `aggregate` and `transform` docstrings of GroupBy are empty, but are more elaborate in the subclasses) (#8231)
- [ ] general clean-up of all the docstrings 
  - especially the `apply` docstring is not very clear to me
- [ ] expand DataFrame/Series.groupby() docstring:
  - clearly list all possibilities for the `by` arg (and provide some short examples in the 'Examples' section)
- [x] document the whitelisted methods: (#8231)
  - this could eg be done by injecting it in the docstring automatically based on `_apply_whitelist`
  - or alternatively by ensuring they appear in the methods list of the GroupBy class (which is not the case at the moment, only in instantiated objects) (see also discussion in #2644)
- [x] More clearly document the DataFrameGroupBy and SeriesGroupBy classes (#8231)
  - at least mention them in the docs
  - one idea is to have a DataFrameGroupBy api pages that just redirects to the general GroupBy page
- [x] Add docstrings to the wrapped whitelisted functions. Eg at present `g = df.groupby(...); g.count?` is returning `<no docstring>` (see https://github.com/pydata/pandas/issues/4500#issuecomment-41220138 for explanation how)
- [ ] Make a clear distinction, about what to expect for the return values of a grouped-apply, e.g. `head/tail/nth` are basically `filter` type of functions, `fillna/shift` are transformers, while almost everything else is a reducer (e.g. `sum/mean/describe`), while `apply/agg` can be any of the above. hmm. maybe needs a separate section for this. (and of course `as_index` just makes this crazy)

If someone wants to tackle this (or parts of this), go ahead!
