I like the way the Amplified Bible puts it. "Love (God's love in us) does not insist on its own rights or its own way, for it is not self-seeking;" This requires quite a bit of prayer and discernment. It's too easy to go too far in either direction.
When we have true, Christ-like love we won't worry about our rights, or privileges. We won't be thinking about what life owes us. Instead, we will think about our responsibilities towards others. We will be ready to help another to the best of our ability. However, we also need to use wisdom. We have a responsibility to God to keep our body healthy. We also have a responsibility to take care of our own home and family. If we get so busy helping others that we let any of those other responsibilities go, we will end up with so many troubles of our own that we will no longer be able to be of any help to anyone. At the same time, if God asks us to do something He will give us the strength to do it. That is why we need to pray and listen. We need to make sure we know what He is asking of us so that we don't go too far, or not far enough.
There's another area where not being selfish actually becomes being very selfish. There are those who are selfish and never give when there's a need for a gift of food, money, clothes, etc. Then there are those who push their gifts on others and in doing so, become selfish. When a gift is forced on someone it is not being given for the person getting the gift, it is being given for the good feelings it gives the giver of the gift. That is when it becomes a selfish act.
Love is not pushy, demanding, or inconsiderate. It thinks of the other person's feelings and needs. Love is ready to help and serve others, but not at the expense of harming someone in the process. True love goes to God in prayer and asks for His guidance. Then it listens, with an open heart and mind, for God's answer.
Again, the best examples we have of unselfish love is in the saving Grace of our Lord and Savior. We don't deserve it. We throw it in God's face every time we chose to ignore God and follow our own desires. Yet He continues to offer it to us, freely giving it whenever we ask.