What does the Bible say about the raising of hands in worship, or saying hallelujah?

There is certainly nothing inherently wrong with the raising of hands to praise the Lord or with saying, Hallelujah. My recommendation here is to pay attention to the common practices of the church where you attend. Some churches are quite comfortable with such displays as long as they are not done to put on a show or bring attention to yourself. These can be honest expressions of praise to God.

However, in other churches, such displays will bring much undue attention and may create tension in the church. These churches are fearful of any display that leans in their eyes toward charismatic practice. Though amen's are fairly common in our church (not extreme) and though we occasionally have someone lift a hand in praise, we are probably of the more conservative group. We emphasize congregational singing as an act of worship. Our people sing robustly and the words of the hymns often declare God's praise.

But I know of very good churches that are much more vocal in their praise than we are. They may see our relative quietness as a lack of the Spirit, though I do not believe it is. In fact, we have a tremendous spirit in the church that certainly comes from the Holy Spirit. On the other hand, I look at some of the churches where the praise is very vocal and wonder where the true praise stops and the fleshly show begins. The truth is, this has been a problem in the churches since the time of the apostles. I do not think that there is an easy answer. We just need to be careful.

I think the best course is to avoid the two extremes. We should never allow our services to become a contest of fleshly display. But neither should they become a graveyard of dead spirits. For your case, I think it best to learn to praise the Lord as befits the church where you attend. God can be truly worshipped in many ways. In the end, it is not the outward actions but the inward heart that exalts the great God.