Whatever you do, never describe the MC as smart. Show it with actions, make him/her come up with plans an solutions to problems.
The moment you start mentioning he is smart, people will go, "yeah, sure, pft" and you will never recover from that.
edit:
Don't even make other characters say he/she is smart in the story. Avoid that at all costs. Just make him/her into a problem solver. People have a weird fetish, feeling that if an MC is mentioned to be smart, they have to debunk it at all cost. It is some weird, psychological stuff that compels readers to try and prove the MC is dumb in fact.
I agree with never saying the character is smart, but not that people have a fetish for tearing the character down when they say he is smart.
I think that instead people are repulsed when the author constantly says that the character is intelligent, because it is the only way he has to prove it, they see that the author is not able to do what he wants to create so the only thing he can do is a "trust me, he is intelligent" although he never shows how.
Now, there is not just one way to show that a character is intelligent; there are several types of intelligence.
You can demonstrate that a character is intelligent by showing how he remembers important things or knowledge of various disparate subjects much better than the rest. There are many people who like to gain new knowledge even if it is outside their areas of work, for example a blacksmith dwarf who knows a lot of literature or ancient history about elves.
You can also show that someone is intelligent by simply showing that they are curious, when they see something they don't understand they immediately get to work trying to figure out what happened. There are people who are motivated to discover new things every day, and it goes a bit hand in hand with the previous point.
My favorite way to show an intelligent person is to show that he is a resourceful person, the macgyver guy who's in a predicament and improvises his way out with whatever he has on hand. Knowing what to do and how to use limited resources, as well as being creative with them when working with them is another way to show that a character is intelligent, plus readers love to try to get them a solution with the resources that the protagonist has at hand and see if he does the same, and in case they did not like it also to know what the character (the author in the background) did with the same resources.
Also, as they said above, being persistent is another way to show that a person is intelligent. A simple way to show intelligence is to recognize that the character does not overlook information or assume things, people might overlook important things that someone curious might not. My favorite series Monk, it's about a very strange detective, he has a thousand different phobias, and he's not very intelligent, but at the same time the guy notices absolutely everything, which leads him to quickly understand what happened in a crime. And the best part is that they show the viewer the same scenario before he speaks to see if one is able to notice the same as the protagonist.