Tithing is a rather simple issue. You can solve it with one verse (which one person has already shown), or you can expound on it. Both approaches will bring you to the same conclusions.
The easiest way: 2 Corinthians 9:7 is one verse that shows the New Testament Christian God's philosophy on giving. It tells us basicly not to give by law (out of necessity). We are told in the James that were are under the "law of liberty". We are told in Gal 3, that were are no longer under the (Mosaic) Law, and that those who are are under a curse. It reaffirms that the Law was went to show us our wrong and bring us to Christ. Now that we are under Christ we are no longer under the law. Heb 8:13 tells us that we have a new covenant. Making the old obsolete. Now that which is obsolete is fading away and ready to dissapear. Since there is no New Testament mandate continuing the Law of the tithe, we are no longer under it. Instead as we see in 2 Cor, God wants us to give cheerfully. Not to give because we have to, but because we know he has lavished His gifts onto us and so as a reaction of love toward Him we will also spend those gifts. As we see with the New Testament church, they gave where they saw need. When the church in Jerusalem was in trouble, Paul went around to the churches to gather up money to help them. As we see elsewhere, we are told to take care of our own, even our own house, for if you don't take care of your own (It says) you are worse then an infidel. So provide for your family, then provide for the Christians around you in need, then give to other needs you find. Once the church was started in Acts 2, you don't see them giving to a "church" expect when that church was in terrible times. In famine, without food, without water, etc. So give where you see the need.
Now as far as tithing as praticed in the old testament. We see in the Old Testament, that their tithe was a food offering. They ate their own tithe with the priests and all the lowly of the city. We even see a place with it says that if you can not bring all the food to the temple, exchange the food for money. Which I sure leads many to believe it can be money. Then if we go on it says, then when you get there buy food their and go into the temple and eat it with the priest, widow, orphan, etc. Be a Berean. Search the scriptures for yourself. It is obvious, but if you have any questions, or if you want more references to look up tithing on (in the Bible), feel free to ask.
Remember, in the Old Testament they HAD to give 10% to God. In the New Testament, we are told to give 100% to God. Not just our food, or money, but our life. If you are sold out to God 100% then you will give as God leads you. That could be 1% or 100%, but you will do as God leads you cheerfully. So don't let 10% hold you back from giving all that God wants you to. And don't let it put you in debt because God told you to pay your bills than give what's left.
Elijah (Acts 17:11, 2 Tim 2:15)