Generally the subject is the focus, but it really depends on your creative vision as to how you balance the background and the subject in frame. How blurry the background should be, how wide the frame should be beyond the subjects and where in the frame the subjects should be are all artistic choices that don't have a "right" answer.
Close up shots focus on the subject and simply casually show where they were. Shots that make them a smaller portion should be emphasizing the scale of where they are and are often trying to capture their experience of being there. Either is correct depending on the goal of the photo. If you are going for a shot that focuses more on the landscape, make sure that you photograph the subject in such a way that it shows them experiencing it. For example, two lovers off to the side of the image looking out over a sunset on a scenic vista. You don't put them in the center of the frame, you put them to the side to show what they are seeing and how they are experiencing it.
Sometimes you can also end up treating the background as another subject. If it's a particular monument or statue or even a building or geographic feature if far enough in the background, then it is often possible to treat the background elements as another subject of the shot and compose the shot around all the subjects. This often can result in a more traditional portrait look, but there is also a ton of room to be creative with it as well.
The biggest thing you will need for shooting subjects in outdoor settings is keeping either good lighting conditions (primarily morning and evening, preferable right after sunrise or right before sunset (known as the golden hour, though it isn't actually an hour). If you can't shoot during the golden hour, you still want to avoid mid-day if at all possible. It will also benefit you greatly to have some powerful flashes that you can use to provide fill lighting against the harsh shadows you can get when shooting in sunlight. This is particularly critical if your subject is going to be at all backlit with a bright background relative to their brightness.