This is a difficult question to answer because it deals with subjective experiences. Nevertheless, we can try to answer it.
Generally, love is understood to be a feeling of euphoria, a feeling of some sort that brings a sense of well-being. However, biblically, love is the concern and action that seeks the best for others. John 3:16, "For God so loved the world that he gave his only begotten son that whosoever would believe in him would not perish but have everlasting life." Notice it says that God's love gives. The nature of love is to give. It is "other" focused.
So, in order to experience God's love we should not look to a feeling, but to that which fits the best description of the other-centeredness that God declares in his Word. In Christianity, the greatest example of the experience of God's love is in the person of Jesus Christ who died on the cross for our sins. God loves us so much that he took our place on the cross and died for us. Jesus said in John 15:13 that the greatest act of love is to lay your life down for another. This is exactly what Jesus did for us.
So, to experience God's love is first of all to trust him by faith, to trust in the sacrifice of Christ on the cross on our behalf. By trusting in Jesus, by looking to Jesus alone for the forgiveness of your sins through his death, burial, and resurrection, you can then receive the forgiveness of God and experience his love for us.
There is, however, another way of experiencing God's love. All across the world Christians have had times when they have "sensed" the presence of God in a very real and powerful way. Since God is love (1 John 4:8), to experience his presence is to experience his love. This experience is often humbling and serves to reveal our own sinful natures, because when we are in the presence of love and holiness, we are "undone" and we see ourselves as we really are. This is an enigmatic experience because it both brings us to tears and engulfs us in his divine presence. This is not very common, but it is experienced by Christians regularly.