I'm having one of those moments, I just can't remember how to say it. By air, by water, by ground? Or is it by airplane, boat, and car? I was reading about an island where the writer was saying "the island can be reached by kayak" so it got me thinking. Thank you for your help.
If we say 'I'm going by air' this is perfectly acceptable but does imply the use of some sort of aircraft (since none of us can really fly without one). Similarly 'I'm going by water' usually implies some sort of boat or ship.
However talking about travelling on dry land is a bit more complicated. The most general term is 'going (or travelling) overland' but this implies either a long journey, a degree of hardship or a combination of the two. We would be unlikely to say 'I'm going overland from Manchester to London', we would be more likely specify the means of transport by saying 'I'm going to London by train' or I'm driving to London'.
These last two are examples of the other way we talk about means of travel where we specify the method more or less specifically. The 'can be reached by kayak' usage is an example of the extreme end of this. 'Can be reached by small boat' is rather more general but does exclude ships, ferries and even yachts and cabin cruisers.
The 'overland' category includes lots of sub categories ranging from 'on foot' through 'by bicycle', 'by road' and 'off road' to 'by train', 'by bus' and 'by taxi' and even 'by public transport'
The only expression in the question which is not idiomatic is 'by ground' This would either be 'overland' or, usually, something more specific.