There are many instances in which Muslims and non-Muslims date, fall in love, and even get married. Very traditional and strict Muslims are often (but not always) against the concept of dating entirely, especially dating non-Muslims, but there are a lot of real world examples of Muslims in happy relationships and marriages with people of other religions.
Learn about Islam if you don't know about it already. Islam is a complex and ancient religion. There are a lot of things about this religion that you may not understand at first. However, in order to truly love your Muslim partner, you should make the effort to learn these things, for example, prayer rituals. Muslims pray numerous times a day. Often, a Muslim will stop what they are doing in order to move aside and pray. Another thing that you will have to learn about are Islam holidays, such as Ramadan (a month-long fast). If you can understand and appreciate Islam fully, you will have a much more fulfilling and connected relationship with your partner.
Be understanding. If you are not Muslim yourself, your significant other's family might object to you being involved with their son or daughter. That is because traditionally Muslims are expected to date other Muslims. It is slightly more acceptable for a male Muslim to date outside of his religion than for a woman. If you understand this at first, maybe you will be able to develop a relationship with his or her family that will lead to a mutual appreciation.
Talk about your future plans. If you plan on eventually marrying and raising children with your Muslim partner, you should definitely discuss which religion you plan on raising your children as, if any. This is to avoid further problems from arising down the line. It's better to have everything carefully planned before you start getting serious.
Learn about your Muslim partner's homeland (if they are not from the U.S.). There are a lot of American Muslims, but if your Muslim partner is from a country in the Middle East, Malaysia, or any other country in the world, it would be a great idea for you to learn about their background. Cuisine, music, arts, tradition--there is no greater way to show love for someone than to show interest in who they are and in their background.
Be sensitive. Be respectful of your partner's religion and don't make stereotypes. Don't make insensitive comments, as no one likes insulting comments, especially from a loved one.
Accompany your loved one to a mosque or any type of place where you feel like you might get a chance to be immersed in the Islam religion. Seeing things with your own eyes might make you develop a greater love and understanding for the religion, which may therefore turn into a stronger love and appreciation for your partner.
Relationships between individuals of drastically differing religions can be tough at first. You have to be prepared to do a lot of work and talking. However, if your relationship is strong enough, you will survive it and end up stronger than ever in the end.