We have already seen the palace at Versailles. We didn’t learn until later there were many more gardens and fountains. How do we go about seeing the gardens that we missed?
You just get on the train and go to Versailles.
You don't have to have a ticket to enter the gardens, but if you want to see the fountains, there is a charge for this.
http://en.chateauversailles.fr/plan-your-visit/tickets-and-prices
In my opinion, it's not worth the time it takes to get to the fountains, but you may disagree.
The RS Guide describes where and what time you can enter the gardens without going through the palace. You can also get that info from this site http://bienvenue.chateauversailles.fr/en/gardens/access
If you click the "Getting Around" tab you can get info about the Little Train and the Electric Car hire (i.e. golf cart rental). The latter are for hire at the Parterre, outside the palace, so if you enter from the garden for free you have to walk all the way up to the palace to rent. Once you turn in your rental, though, I believe you can exit by the palace -- you don't have to walk all the way back to the garden entrance where you came in.
Comments on this forum seem to indicate that the musical shows are not really worth it, but YMMV.
We did the gardens only on a fountain day in October a couple of years ago.
https://janettravels.wordpress.com/2016/02/15/fountains-of-versailles-a-little-chaos/
The gardens are really beautiful when the fountains are going and IMHO well worth a visit. The fountains run for an hour or so in the morning and then an hour and a half or so late in the afternoon. Between these times you can visit the wider estate, the Trianon, the Hameau, row a boat on the canal etc. The ticket is good all day to leave and re-enter the gardens.
There were no lines to speak of to enter the gardens; the entrance is to the right as you face the chateau and around the bullding. I wouldn't make the trip on. a non fountain day for the gardens.
Don't just walk through the gardens...rent a bike! The grounds around the palace are huge and, once you get past the bottom of the formal gardens, the crowds thin and you can find beautiful places that you will have completely to yourself. Wheat fields, long avenues of trees, forests...it's lovely. You can rent bikes right next to the grand canal in the back of the palace. It's one of my favorite things to do in France!