"'But when you give to the needy, do not let your left hand know what your right hand is doing, so that your giving may be in secret. Then your Father, who sees what is done in secret, will reward you.'" NIV translation
In contrast to the religious, we are to be so secret about our giving that nobody knows. They want to glorify themselves while we are called to glorify God. We trust that God will reward us for our actions and that reward will be better than any fame or fortune we can get in this world.
"'And when you pray, do not be like the hypocrites, for they love to pray in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full.'" NIV translation
The second act of the righteous is praying and, once again, we see that it is not if but when we pray. The religious leaders of the day would make a big show of praying loud and in public so that everyone would see how righteous they were. The same type of thing happens even today in the meetings. Once again, Jesus says that they have received the recognition that they were looking for and that is all they will receive.
"'But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you.'" NIV translation
In contrast to the religious, the truly righteous are to talk to their Father in private. In the past, God dealt with nations and groups of people but, through Jesus Christ, we have a personal relationship. We keep other personal conversations private and it should be the same with the time we spend talking to our heavenly Father.
"'And when you pray, do not keep on babbling like pagans, for they think that they will be heard because of their many words. Do not be like them, for your Father knows what you need before you ask him.'" NIV translation
Now, Jesus speaks of the method of prayer and it is contrasted to the way that pagans prayed. They would repeat the same prayer to a list of so-called gods in hopes of finding the one that could help. The righteous know that God can and will answer the prayers as well as the fact that He already knows our needs.