In practically every aspect of life, we're constantly having conversations whose sole purpose is to provide information. We wouldn't dream of trying to "hide" an explanation in some other, unrelated conversation. In film, though, that's exactly what we have to do.
And let's be frank here. It's a major pain in the ass.
But it's also essential. No matter how seamlessly we weave our narratives, there are moments where we sit back and realize the audience doesn't know something that we need them to know, and we need to find a way to tell them.
In general, screenwriting is a swing-for-the-fences kind of pursuit. You put your all into it and try to deliver your very best, and in doing so you accept the possibility of abject failure. Writing exposition? Not so much. This is an area where you're actively trying to not screw up. No one's going to say, "Holy shit, that was some awesome exposition!" if you do it right, but people will most definitely say, "That exposition was fucking terrible!" if you do it wrong. In other words, it's better to aim for okay exposition and land on target than to aim for incredible exposition and miss.
And let me clarify here, because there are two ways to "miss" -- by being too obvious, or by not being obvious enough. It really behooves us to avoid both these landmines, because the former exposes our writing as amateurish, while the latter will result in mass confusion due to the reader/audience missing important information.
I think the easiest way to screw up exposition is by failing to couch it in any kind of conflict between characters. No normal person would greet a friend by saying, "Hey! If it isn't my favorite Harvard-educated psychiatrist!" On the other hand, given the right argument, that person might choose to throw that piece of information in his friend's face. "You're calling me a loser? You, the Harvard-educated psychiatrist who still lives with his mother?"
Another common technique is bragging-as-exposition. "Look, you don't need to dumb it down for me. I'm a Harvard-educated psychiatrist." I'm not as much of a fan of this method, but in the right context it's not so bad.
Here's one we've all seen ad infinitum: the "I've done my homework" speech. "You think I don't know you, wise guy? Two years of community college in Indiana, medical school in Barbados, cheated your way through the boards. Not only is that Harvard diploma in your office a fake -- I can even tell you the website you ordered it from. Wanna hear what else I've got?"
A close relative is the "emphasizing a point" technique. "I can't lie to him about being pregnant! He's a Harvard-educated psychiatrist, he'll see right through it!"
These examples are some of the old reliables. They're not entirely subtle, but they get the job done. There's no chance we would miss the information that this character is a Harvard-educated psychiatrist (or at least claims to be).
And these are by no means our only choices. They're fallbacks -- relatively painless ways to shoehorn in a bit of information without changing too much else or creating a new scene. It's okay to use them once in a while, but if all our important exposition is coming out through one of these methods, the whiff of amateur is going to be in the air pretty quickly. The best way to convey exposition is almost always visually, and in this case it wouldn't be hard to do that (one five-second shot of the character sitting in a chair across from a patient on a couch with a Harvard diploma in the background takes care of it).