Be quiet. And that doesn’t mean that you are no longer expected to share your feelings and tell jokes and engage in conversation — it just means be quiet. Sometimes, quiet is needed. Learn to appreciate what quiet can be for people. Learn how two people can sit on different sides of the room, silently engaging in their own activities, and still achieve a profound sense of closeness. Understand that sometimes they will need their alone time, but that often it can be supplemented with that sense of empathetic quiet. If they feel that they can just be themselves around you (and not placate everyone in the room with some overblown song-and-dance routine of “look at how social I am”), you will have already won.
Teach yourself that the association we’ve always held with the introverted and the pathologically anti-social — the people who are supposedly incapable of enjoying the company of others and thus retreat into themselves — is a faulty one. Yes, someone can need quiet time by themselves to recharge from a day’s activities, but that by no means implies a deeper level of anxiety or disdain for those around them. Work to rid yourself of the stereotypes and misplaced mockery that has been lobbed at your beloved introvert since the first day they entered kindergarten and realized just how much they needed nap time after a few hours of working in groups. Realize that wanting to have those few minutes of “nap time,” the moments of recharging and calm, have nothing to do with wanting to escape you — they are only intended to make spending more precious time with you all the more pleasant.
Do not force them to engage in constant activities which you believe will make them a more “well-rounded” person. While there are always compromises to be made in terms of events which are important to show up to or people who are worth making effort for, you must clear your mind of the idea that someone is automatically a better and more whole person if they go out more. Understand that, just because we have gotten used to bars and parties and trips out on the town as our leisure activity of choice on the weekend, does not mean that everyone finds it as universally cathartic. Find the balance between going out and staying in which feels comfortable for everyone.
Enjoy the rich inner life that can often only reveal itself when an introvert has met someone with whom they feel unfailingly comfortable and open. Realize that there are so many people for whom their thoughts and ideas are presented in the tiniest tip of a social iceberg, and that you happen to be in love with one of them yourself. Spend days, weeks, years plotting out the various points of the massive presence which lives just below the surface in their mind, and feel the profound privilege bestowed on you to be the person with whom they have decided to share everything they’re normally not inclined to reveal.
Expect there to be difficulties of understanding. Expect there to be times when what you consider a “normal” amount of socializing proves to be too much in a way that is difficult to empathize with. But prepare yourself to love this person regardless of the minor inconveniences that love might present. Because the love you share with someone that other, less deserving minds would deem “shy” or “weird” is something that is offered up every day, something that takes effort and conscious compromise on their part. For an introvert, letting someone into the small space which you have forever claimed as your own to protect your most basic needs of comfort is a huge risk. And they love you for having taken it. Never forget to show them that you love them back, and that you’re more than happy to let them be alone with their tea for a little bit if that’s what they need to do most. 
