恋爱(liàn ài) - romantic love, a romantic relationship in Mandarin

恋爱 (liàn'ài) is romantic love as a state you are in, not a feeling you have. The phrase to memorise first is 谈恋爱, literally to talk love, which is how Mandarin says to date or to be in a relationship. 他们在谈恋爱 is the natural way to report that two people are together.

Around it sit the words it is not. 爱情 (àiqíng) is love as an abstract subject, the thing songs are about. 爱 (ài) is the verb you use towards a person. 恋爱 is the relationship itself, with a beginning and an end, which is why it takes 一次 as a counter: 谈过一次恋爱 means having been in one relationship.

The trap is trying to use it transitively. There is no 我恋爱你; that is 我爱你. 恋爱 takes no object at all, because the other person is already built into the meaning. If you want the object back, use 爱上 (àishàng, to fall in love with) instead.