Getting to Versailles on the train is relatively easy. I went from somewhere fairly central and the only complication was working out which platform to use when the station was on a circle line where both sides went towards Versailles, but one way took about 30 minutes and the other over an hour.
Tickets you buy from a machine and can ask for the machine to use English. We flew in from CDG, so you'd just get a different train from your starting point, probably one of the RER lines.
Then it's about a 5-10 minutes walk from the station, but it's signposted. When you get to Versailles, there are timed queues for the palace. Like all good Brits, I saw a queue and joined it, thinking it was the queue to get into the whole complex and it was only after I'd stood there for about 10 minutes did I realise that it was the timed queue for going inside the palace and to get into the gardens, you went round the side.
Book your tickets online. I made a bit of a mistake because I didn't realise you can't go back in the same gate to go back in the gardens after the palace so I hadn't finished with the gardens when it was my slot to go into the palace. You can go in a second time via another gate, but it's a long walk round, so you might not want to do that. If I was doing it again, I'd go in the palace first, fairly early in the morning, then spend the rest of the day in the gardens. There were cabins dotted around inside selling food, but I don't know if they'll be open in winter.
I found travelling around on public transport fine and easy to use. I went with DP while he was working there and I had nearly 2 full days to just wander round on my own.
The first day I just looked around all the sites, went in the Marie Curie museum, parks, including one with the Statue of Liberty in, Pompidou Centre just for a hot drink (it was freezing when I was there) walked miles around just looking at stuff. The second day I went to Versailles, which took all day.