Is This How the Points 'Trifecta' Game Works?

I've been doing lots of reading/watching lately about people who accumulate points and miles and then redeem them for first-class flights for a fraction of the full price of that ticket. I'm curious as to how they play the game. Is this what they do?

1. Get a few transferrable points cards, such as the 'Chase Trifecta', 'AmEx Trifecta', etc.
2. Spend enough to get the welcome bonuses, which means spending $5000.
3. ~~Get another airline card. So to use Chase as an example, I'd also get the United Explorer card. You can spend another few thousand here to get even more welcome bonus points.~~
4. ~~Transfer the points to the airline card, and~~ accumulate more points by spending on the cards. *Use the Chase/AmEx/etc. portal to find flights using points.*
5. Because the airline is likely part of an alliance, you can book a flight with a different airline within the same alliance network. So, to use United as an example, again, it's part of the Star Alliance, so I can use it to book flights with other airlines, like Lufthansa or Air China, for example.

Here are my questions about this game:

* Is this correct, or am I missing anything?
* If so, can one really book any flight from any airline within the same alliance network?
* How do I decide what airline to use as my airline card to transfer the Chase/AmEx/etc. points to, so I can then transfer to whatever airline I want within the same alliance network?

**EDITS: Made corrections as comments have come in. Incorrect information is struck through and new information is italicized.**