Gemini are easy once you get the hang of the concept of the Gemini Summon.
They're just monsters you can normal/special/tribute summon like any other monsters (the different summons according to level and situation, of course). To get the effects of Gemini monsters, you perform a Gemini summon by using your normal summon for the turn (or a card that grants you extra normal summons). During most turns without using any effects, this means you would have to have the monster on the field (either face down or face up) for at least a turn. Monsters that are level 5 and above can be Gemini summoned without using any tributes. It's a pretty straightforward concept.
They also have a bonus in that they are counted as Normal monsters while in the hand and graveyard, so this eases getting them onto the field with special summon effects.
It just kinda sucks because they're the most vulnerable when you Gemini summon them. Trap holes, Torrential, summon negation, and Book of Moon can all backfire hard when you attempt to Gemini summon (and, in turn, using up your normal summon for the turn). Thankfully Geminis got a boost in the Warrior's Strike structure and they can be pretty silly if you've got a solid enough deck for them.
P.S. - You are pretty much on the mark for synchro monsters.