Yes, we should give to God. I am completely sure about that. Wasn't Jesus himself looking at how people gave, noticing that poor widow give all she had? That is one proof that even in the New Testament, after God has made a new covenant with us, giving is still important. You can't just go on living however you want, spending all you want to and knowing that God forgives you no matter what if you repent. Yes he does, there's no doubt about that, but it's not like you don't have to obey Him. Yes God has made a new covenant with us by dying for our sins on the cross, but it does NOT mean that the entire Old Testament is somehow canceled. It only means that now, you don't have to obey the Law brought to the people by God through Moses, to be saved. Just think about it. Because there's New Testament... it doesn't mean you don't have to obey the Ten Commandments, does it? Do you say it's ok to murder or to covet what's no yours because it was said in the Old Testament? I don't think so.
Now more on the giving part. I firmly believe there are two parts of that. There's tithing, which is giving God 10 percent of everything you have, and then there is the seed. Which is your freewill offering if you may. It's something that God places on our hearts to give. I believe we should tithe, for the 10 percent of what you own does not belong to you - it is God. Just think about it. The Earth and everything in it belongs to Him. Every gift you have in your life comes from above, from His generous hands. Nothing is yours, but this 10 percent is special. It is something that you use to show God your obedience, humility, and thankfulness for what He is doing in your life. This money is simply not yours. It belongs to the Lord. It is up to you to honor this or not.
Now about the seed that you are planting. It's your freewill offering to God, which can be given to your church or any other ministry/church that God places upon your heart. It's how you honor God and the work He is doing with His people in any given church.
These are simple ways to honor God. These teach you humility, these teach you to say no to some of your own passions, and finally, these help you to find financial favor with the Lord. Many a time in my life I was completely broke but somehow still managed to fulfill my duty to God by tithing and giving, and He has come to my rescue when I thought there was no way out. I am by no means saying God will not uphold you if you do not tithe and/or give, it is just my testimony. God has provided for me miraculously in my life as I tried to stay faithful to him with my finances.
By posting this, I am not forcing my beliefs on anyone. It is up to you how you do this. But it's my testimony and my firm belief. I hope it helps somebody else on here.