You need several things:
1) Massive fleet. Even if you don't want to use it, you need a fleet or the AI will attack you. Often many of them at once. Note that war is often not avoidable, but you can end them without overrunning an enemy. Fend them off for a dozen turns then sue for peace.
2) Diplomacy. The way to have civs not get pissed by your influence bases is to be allied with them, or do it commando-style. If you're allied with them, they won't complain no matter what you do. For the commando raid, build a couple dozen constructors, get them to a system near your border, build four maxed out bases touching the habitable planets and flip them in a couple turns (note this does not mean "have all the planets in the area of effect of the starbases", it means "build the base in the square next to the planets". Commando style flips the planets before the AI can get pissed about it, but it pretty much requires #3.
3) Assuming you are playing TA, be evil. The Mind Control Center was fixed to do what it was always intended to do; that is, instantly flip any planet that hits an influence ratio of 4. If you are not playing TA, DO NOT build the MCC - it actively prevents planet-flipping.
4) Get all influence mines in existance. Boost to you, denies same boost to others. Pretty straightforward, although getting a mine from someone can often be anything but straightforward if you aren't willing to destroy their base yourself.
There's a few other minor things to focus on, but those are the primary ones. Especially #3, I once flipped 40+ planets in the first turn after I built that. The following cascade of flipping took another 80+ in 10 turns and destroyed 2 or 3 civs entirely by influence.
