You have to keep pressing on one of them and press be romantic, and then it'll have an icon that says something like get married and then you have to buy a ring thingy using the diamond things. and it'll say ask to move in on one of the things you can do with them.
You want make them become 'Good Friends' or 'Partners'. You can do so by making them 'Be Romantic' or 'Be Friendly' to each other untill you can make one of the sims to 'Ask to Move in' to the other. BTW, it is also for Android.