Okay, I recently finished reading an online story called Worm which is about people with superpowers in a fairly realistic (if grimdark) world. The main character of which has the ability to control bugs, but is extreamly successful by making the most of her power (weaving spidersilk clothing, putting pepper spray on bugs to attack her enemies, etc).

There is also one minor character who has the power to grant limited powers to others at the expense of their free will. His name is Teacher (listed in 'Birdcage' on the characters page if you're not afraid of spoilers).

Anyway, Teacher can apparently grant people powers that are less than what a 'true' parahuman would get, but are still impressive compared to what a normal human can do. TvTropes says he could grant things like x-ray vision, limited precognition, spider-sense, along with various technical and thinking skills that make the individual just a step lower than a genuine Mad Scientist. The downside is that the people he uses this on tend to become his thralls, either by being brainwashed into serving him, or because the rush of gaining new knowledge or power is tantalizing and addictive (one character bought technical skills from him on the promise that he would keep his free will, he kept his free will but became mildly obsessed with the thought of getting new powers that he helped Teacher break out of a maximum security prison at least a decade later).

My theory is that the 'make people your thrall' bit is a safety mechanism built into the power, no sense giving a guy expert sharpshooter power only for him to shoot you later.

Anyway, lets say a friend of yours recently gained Teacher's ability. For this scenario, they can grant themselves one limited power at a time to test it out and tweak it for maximum efficiency and then grant that power to willing volunteers. Mainly things like boosted skills, precognition, or clairvoyance or whatnot. No flight, shooting fireballs, or anything flashy.

How would you ensure you didn't get brainwashed if you get a power for yourself, how would you keep your friend from getting kidnapped by supervillains seeking to exploit them, or how would you use this to improve the world (without filling it with brainwashed thralls or addicts)?

how would you keep your friend from getting kidnapped by supervillains seeking to exploit them

It seems like this problem solves itself -- any supervillains who do attempt to exploit this power will end up enthralled or addicted. Or are you talking about supervillains who have already figured out an answer to part A of the question?

Part A is easy to answer as a supervillain; kidnap the guy, lock him in a room with high security and an easily-triggered bomb, bring in mildly untrusted henchmen, make him give them powers or get tortured, then use threats against him and them to control them, keeping him locked away; if a security breach kills him, they won't free him, and you have a lot to gain.

Maximal discipline and focus. Not only do you get a lot done, if you remained at all the same individual, your webs of beliefs and values would have to still be unchanged enough that you could detach from your situation and prioritize what you originally wanted to do over what s/he wanted you to do. It would be very hard to control someone who is at all times mindful of their motivations, drives, and thought processes.
You could also rig up a system beforehand to bind yourself to your original goals, something as simple as reminder notes, or as elaborate as getting a third party to pick you up and restrain you somewhere.

As for the supervillain problem, this person would probably be better off taking care of it themselves, Kaiser Soze style, creating a network of people with the enhanced abilities it would take to keep them hidden, and to properly vet anyone seeking enhancement.

How long does this last, incidentally?

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Giving powers to a henchman you explicitly don't trust seems like a bad idea.

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The powers seem to be permanent until overwritten, along with the brainwashing. The only temporal limit it seems to have is if the power or skill given becomes obsolete by outside forces. Say, if you get the skill of a master surgeon with skills that won't be learned for the next five years, then six years later medical science could advance beyond that and you would need to get the power 'updated' to keep ahead of the curve.

Or similarly, if you ask for the power to defeat a specific Artificial Intelligence and the AI starts growing and adapting itself, then you would need regular updates of the power to handle the newly modified opponent. The power doesn't get weaker, it's just that the world gets more complex and that same power level might not cut it any more.

Though, lets say you get the ability to grant yourself a variety of powers and in turn grant those powers to others. By default, granting powers to others tends to modify their values to make them loyal to you (that's a case of your power trying to protect you, both giving you thralls and keeping them from using their powers against you).

You can however consciously avoid brainwashing people, but no matter how much you remove that 'safeguard', the fact is that gaining powers like these are addictive. The human brain craves information and suddenly gaining Thinker or Tinker powers (as these are called in the setting) would be more appealing than all the interactive media or websites in the world.

I wouldn't go anywhere near Teacher's power. It was one of the creepiest things in Worm for me, and... that's saying a lot. You didn't mention that the granted powers also come with a decrease in intelligence.

one character bought technical skills from him on the promise that he would keep his free will, he kept his free will but became mildly obsessed with the thought of getting new powers

I thought this was explicitly stated to be untrue. Much later in the story, a character with the necessary overview to understand Teacher's power reflects that that promise must have been a lie on Teacher's part and that Teacher in fact couldn't have done that (not to mention that everything we see about the odious man screams that he wouldn't).