Versailles - Gardens, The Hamlet & Trianon Palaces

If I'm wrong someone will correct me but, as far as I know, the only times the fountains are in action are on the 'fountain days' which entails an additional charge (usually the gardens are free). Here's the website with days and ticket prices: http://en.chateauversailles.fr/prepare-my-visit-/single/tickets-and-rates/billets-et-tarifs/les-grandes-eaux-1-en.

I believe the best way to get to the gardens is just to follow the crowd from the train to the main gate. Then entrance to the gardens is on left side of the courtyard - the gate without the line (unless there's a security line there too now).

You can take a shuttle bus or walk around to the Trianon entrance and enter there. You used to be able to walk a bit further and start your visit at the Petit Hameau but it appears that that gate (Porte St Antoine) is not open at present. Either way, it's our favorite part of Versailles.
It's a fairly long walk, but interesting in that it gives you a sense of how big the estate is.

RS covers this in both his Paris and France books.
Here's what it says on the Versailles website http://en.chateauversailles.fr/prepare-my-visit-/single/access:

Entry to the Trianon palaces and the estate of Marie-Antoinette

You can enter the Trianon palaces and the estate of Marie-Antoinette either by going first through the Palace via the Grille d'Honneur gate, or directly via the Queen’s gate or the Saint Anthony gate. Anti terrorist security plan : only the gate of Honor and the Queen's gate are open. Find the gates on the interactive map.

Some bus services stop at these gates:
www.phebus.tm.fr / Horaires / Trajet

We went this fall on a Sunday, fountain day.

Basically, the garden entrance is to the right whereas the chateau entrance line is to the left as you face the chateau as you enter the plaza from the train. You walk around the building to the right and there are booths to buy garden tickets (on fountain days) presumably those gates are just open on non-fountain days. We really enjoyed seeing the fountains in action.
https://janettravels.wordpress.com/2016/02/15/fountains-of-versailles-a-little-chaos/
Once you have toured the gardens, you can exit at the bottom where there are boats to rent, an ice cream stand and restaurants and then go right and walk a good long ways through pleasant woods to the Trianon. (you can use your ticket to re-enter the garden later if you wish; fountains don't run all day but for an hour in the morning and an hour and a half in late afternoon -- at least in October when we were there) Tickets for the Trianon are sold at the entrance, the Hameau grounds are free.

Or you can go back to the area near where you entered the garden and get a tram ride over to the Trianon. We didn't do that so I don't know how much it costs.

At the Trianon you can tour and then exit the back and walk through some lovely gardens to the Hameau and tour that. We then walked back to the chateau/gardens. It is a long day and a lot of walking, but in good weather very lovely.

If you go on a fountain day and enter at the Queen's gate (the most direct route to the Trianons), note that this entry and part of the gardens are free. It's a pretty far hike, but a pleasant walk through town and through the more park-like setting of the gardens (and it is indeed used as a park). But you WILL have to pay to enter the formal gardens on a fountain day if you return from the Trianons past the Grand Canal. Only the formal gardens area are ticketed on fountain days.

If you go into the gardens through the chateau entry, you'll buy your ticket there and can stroll the formal gardens first. Note that the fountains run on a schedule, about 1-2 at a time throughout the day. So it can take hours to see most of the fountains operate. Check to see when your favorite fountains will be turned on so as not to miss them.

There is a restaurant near the canal, a tram out to the Trianons and Hamlet, or you can rent bikes. Since you are not going inside the chateau, perhaps you can bring a picnic lunch to eat down along the canal. You can also rent paddle boats on the canal.

Versailles is a charming town. The main center and squares are on that side of the chateau (the Trianons side). So if you enter or leave via the Queens Gate, take the time to stroll through the town.