You're getting Favoured Class confused with a restriction on multiclassing
Favoured class in pathfinder gives you a bonus (+1 HP or +1 Skillpoint) every time you take a level in the favoured class. Some races have alternate options (like +1 evolution point per 4 levels in Summoner for a Half Elf) that replace that bonus. It in no way makes you unable to take different classes. If you take a class that isn't your favoured class, you simply don't receive the bonus.
Each level of a class is modular, so you can be a Barbarian 1/Fighter 1/Druid 2/Sorcerer 1/Bard 3 if you want, and you'd be a Level 8 character overall (1+1+2+1+3).
Taking a Prestige class is a matter of fulfilling the pre-requisites and then taking the class like any other.
In your case, you need 1st level Arcane spells, 5 Skill Ranks in Kn: Arcana, and not to be a dragon (Dragon Disciple pre-reqs). You can only get 5 Skill Ranks at level 5, so the first time you can enter the class will be at level 6. You'll also need Arcane spells (druids cast Divine spells), so you'll need to either take a feat that grants an arcane spell (there are a few, from memory) or take a level of Sorcerer or Wizard. Or, actually, Summoner. Summoner seems to work better with Druid flavour than either Sorcerer or Wizard.
So you could enter as a Druid 4/Summoner 1, or a Druid 4/Sorcerer 1, and then take your first level of dragon disciple at level 6, so Druid 4/Summoner or Sorcerer 1/Dragon Disciple 1, then Druid 4/Summoner or Sorcerer 1/Dragon Disciple 2 etc.
One hitch in your plan might be that Dragon Disciple only advances Arcane spellcasting, so you couldn't advance your Druid spells by taking the class. If so, you could ask your GM about a homebrewed version - a Forest Dragon Disciple or something, which requires Divine spells instead of Arcane, and advances Divine spellcasting. This is a very simple homebrew and should have absolutely no rules ramifications whatsoever.
Alternately, Summoners are very similar to Druids in some ways, especially with the First Worlder character archetype, which lets them use the Summon Nature's Ally spell instead of Summon Monster, gives them a more fey or animal themed eidolon and generally makes them more 'nature summoners'. They still have Arcane spells, and so qualify for Dragon Disciple.
Either way, let me reiterate, there is no restriction on having only '2 classes' in Pathfinder whatsoever in any way. You can take as many classes as you have levels to spend, although, that might be weaker than sticking to one class and advancing it.