"As in all the congregations of the saints, women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church." NIV translation
This passage is one of the most misinterpreted in all of scripture and has been used to beat down Christian women for centuries. We must understand that Paul was saying that the women, like those speaking in tongues and prophesying, were to be orderly in doing so. The silence that he speaks of is speaking of a temporary silence and not a total ban on speaking. It seems that they may have been interrupting the meetings with irrelevant questions or maybe even gossip. Paul reminds them that the questions could be answered at home by their husbands as that is one of the major responsibilities of a husband (see Ephesians 5). Once again, we are reminded that Paul was teaching the Corinthian believers about the purpose of meeting as brothers and sisters in Christ which was to build each other up in the faith. Therefore, questions that were off topic or gossip would have been contrary to the whole purpose of meeting together. For the good of the body, it was best if those matters were handled in private.
"Did the word of God originate with you? Or are you the only people it has reached? If anybody thinks he is a prophet or spiritually gifted, let him acknowledge that what I am writing to you is the Lord's command. If he ignores this, he himself will be ignored." NIV translation
Paul is referring to the fact that we are all a part of the body of Christ. Parts of the body recognize each other and work together. In the same way, Christians can recognize teaching from God.
"Therefore, my brothers, be eager to prophesy, and do not forbid speaking in tongues. But everything should be done in a fitting and orderly way." NIV translation
Paul sums up this part of his letter by encouraging the believers to seek the spiritual gifts but to remember their purpose. The next time you see someone "speaking in tongues", ask yourself whether it is in keeping with the purpose of the gift or is it some kind of show to make the person appear to be a super saint.