What are the procedures and documents necessary when traveling to France from the UK (not by plane)?

I can answer the rail part: When boarding your train at London, you'll have to pass through customs and security check just as if you were taking a plane.

The platform of the Eurostar train is separated from the other platforms and the only way to get onto it is through the security check and customs.

The UK is not part of Schengen. A UK visa doesn't entitle you access to the Schengen area automatically.

According to this page, however US citizens can enter the Schengen area without a visa, that is given some conditions. The basic requirement is a valid passport. If you want to have multiple entries or want to stay longer then 90 days, you need to contact the French consulate.

There will be entry immigration and customs for france. If you are travelling on commercial transport you should encounter those controls automatically. In some cases the controls are juxtaposed (that is you will be checked by french immigration before exiting the UK).

Having never been rich enough to own a private sea going boat I have no idea what the procedures are like for them.

The UK does not have exit immigration per-se but commercial transport providers are now required to provide details of exiting passengers to the government.

Whether you need a visa, work permit or simlar depends on why you are visiting and for how long. Regardless you should carry evidence of the purpose and duration of your visit.