BUG/DOC: Add documentation in types/common.py
Adds documentation for all internal functions in `types/common.py`

In addition, caught a bug in which some functions calling `_get_dtype` were not catching the `TypeError`.  Documented those functions along the way too.

Partially addresses #15895.
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=h1) Report
> Merging [#15941](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/6d90a436674a1e285d4577553b5cb75906a1bd27?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/15941/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #15941      +/-   ##
==========================================
+ Coverage   90.98%   90.99%   +<.01%     
==========================================
  Files         145      145              
  Lines       49556    49565       +9     
==========================================
+ Hits        45090    45101      +11     
+ Misses       4466     4464       -2
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.76% <100%> (ø)` | :arrow_up: |
| #single | `40.56% <37.5%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/types/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=tree#diff-cGFuZGFzL3R5cGVzL2NvbW1vbi5weQ==) | `94.48% <100%> (+0.83%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=footer). Last update [6d90a43...aa9ec1b](https://codecov.io/gh/pandas-dev/pandas/pull/15941?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments). thanks @gfyoung 