I have just bought a couple of extensions for Tropico 4, but I don't understand how to switch from one to another. It seems I am stuck in Modern times. How can start Tropico 4 with El Plantador instead?
El Plantador is always enabled
El Plantador is a very small DLC; it only adds a new building, a new avatar, a few decorations, and a new mission (which is separate from the main campaign and the Modern Times campaign). The building, avatar, and decorations are available in all games, whether they're Modern Times or not. It should already be enabled if you've bought it; if you can build a Plantation (in the Food/Resources section), then it's enabled.
I've bought both Modern Times and El Plantador, and I'm currently playing the Modern Times campaign while building Plantations, so the two DLCs work together just fine.
Turning Modern Times on and off: only in sandbox games.
The Modern Times DLC adds two things:
If you don't like Modern Times, you can turn it off in sandbox games. For scenarios, you're stuck with whatever the scenario creator chose. If you don't want to play with Modern Times, play scenarios that don't use it.
The "Challenges" (scenarios created by random internet people) are broken into two groups: Modern Times and Not-Modern-Times. There's a selector at the top of the screen when you're looking at the challenges.
Almost all of the scenarios under "Extra Missions" are non-Modern-Times.
(There are a couple of minor bugs when playing non-Modern-Times games, mostly around random reputation-raising missions from some character that request a Modern Times building or edict, like the Telecom building. Just dismiss those missions instead of accepting them; you can't fulfill them. This might be fixed by now.)