You can either do an in-situ paint job with the door attached....
Or the longer, more perfectionist route, which involves a bit more work and trouble, by taking it off it's hinges, lying it flat somewhere (on two trestle/saw horse stands) and being able to prep and paint it and leave it to dry in a dust/dirt free environment i.e not outside.
It depends on your time and effort.
It also depends on the finish you want. Do you want to see the wood? Or do you want a gloss finish?
Before you start you need to need to strip it (heat gun or dip or chemical (the latter is not too effective these days)).
Then sand it back to bare wood, repair any damaged with brown filler and apply a few coats of varnish in your preferred stain.
If hard wearing
oil based gloss, you want to sand it back, repair damage with a filler, apply a primer, a few layers of undercoat (with a quick sand between each layer) and then a top layer of gloss paint. Don't go too thick on the gloss too quickly. You could even do two thin coats with a light sand after the first layer. ensure you leave enough drying time between coats.
If you do not want to use an oil based gloss, there are water based alternatives.
Barn Paint and Sadolin Superdec spring to mind. You can only get a gloss in black and white with Sadolin. They do have a Satin in a variety of colours.
https://www.sadolin.co.uk/product-category/professionals/opaque-timber-protection/
Bdec Barn Paint has a variety of colours in a semi -gloss.
https://bedec.co.uk/bedec_products/barn-paint/
They may be not as traditionally hard wearing as an oil based gloss, but I have seen posts of pro decorators painting beach huts with this stuff (both of them).
A water-based gloss may not have the pop of an oil gloss. But, it will be a lot easier to deal with. You may have to do a few more coats to get the depth of colour you want. If you prep to a good surface you may not need a primer with those two, but you can check the spec sheet. I know Superdec states it does not really need a primer, but they do have one.