1tim1:20 says that he/Paul gave some people into the hands of satan so they learn not to blaspheme. My question is-how did he have that power? Do all Christians have the power to hand people to satan?
That's a good question, but it's probably impossible to answer with any sense of certainty in that we cannot positively identify exactly who Paul was speaking of even though he gave us their names.
I Timothy 1:18-20
This charge I commit unto thee, son Timothy, according to the prophecies which went before on thee, that thou by them mightest war a good warfare;
Holding faith, and a good conscience; which some having put away concerning faith have made shipwreck:
Of whom is Hymenaeus and Alexander; whom I have delivered unto Satan, that they may learn not to blaspheme.
This Hymenaeus is probably the same Hymenaeus whom Paul mentioned in his second letter to Timothy, but that's not guaranteed.
2 Timothy 2 verses 16 thru 18
But shun profane and vain babblings: for they will increase unto more ungodliness.
And their word will eat as doth a canker: of whom is Hymenaeus and Philetus;
Who concerning the truth have erred, saying that the resurrection is past already; and overthrow the faith of some.
Making somebody's faith shipwreck and overthrowing somebody's faith could be the same thing and both could have had to do with Hymanaeus' heretical belief that the resurrection had already past. If it is the same individual, then turning him over to Satan could have simply meant that Paul had him excommunicated or removed from under the protective shadow of the church.
Properly identifying Alexander is even more difficult. Paul did mention an Alexander in his second letter to Timothy as well, but this Alexander doesn't seem to have been a member of the church, so delivering him to Satan, if it's the same person, would seemingly involve something beyond excommunication:
2 Timothy 4:14-15
Alexander the coppersmith did me much evil: the Lord reward him according to his works:
Of whom be thou ware also; for he hath greatly withstood our words.
I'm personally of the belief that this is not the same Alexander whom Paul was referring to. I mean, if he was an unbeliever, then Satan would have had him in his control already, so I fail to see why Paul would have had to deliver or turn him over to Satan who already had him in his power. Some people also consider that this Alexander is the one mentioned in the book of Acts chapter 19 verse 33, but that seems highly unlikely to me.
Basically, my somewhat educated guess is that these two were Christians at some point in time who got mixed up in heresy and were excommunicated or turned over to Satan. That said, it is still just a guess.