The admins haft to promote your take, nothing you really can do to get them to promote it, just sit back and wait to see if it gets promoted. As for how long it takes the amount of time can vary, my take only took a bout an hour after being posted to get promoted.
The admins decide which myTakes get promoted. In the FAQ, it says, "promoted myTakes are featured myTakes that we found to be really inspiring or helpful, full of information that we want more G@Gers to learn from!" However, I've seen a lot of promoted myTakes that are not inspiring, informative, or helpful so, I'm not sure what exactly makes them actually decide to promote a myTake.