skateboarding = riding and doing tricks on a skateboard, which is a board with skate wheels on it [see here:
http://tinyurl.com/2o9hsm].
Skiing is moving over snow on long boards, one for each foot [see here:
http://tinyurl.com/2j6pa8]
You go
to the gym and go
on a run, but you can also say
I go to a gym and am going to go on the run. It will depend on the context and related questions.