If you do it right, by the time you get to the boring parts, they won't be boring any more. Personally, I'm trying to get the knack of not running any exposition unless the reader's already interested in it. You run some exciting bits first, because exciting bits are exciting, and while you're doing that, you build up curiosity, which you then satasfy in bits with exposition.
There's another warning of how not to start...
There are a large number of fanfic authors, especially really shippy authors, who love to write about their favorite characters *being* together. That bit at the beginning where they *get* together is just a regrettable obstacle that you have to slog through to get to the good stuff. It's rushed, and poorly thought out, and poorly justified, and it shows. Don't give us the beginning that you have to get through to get to the good stuff. If you don't enjoy writing it, we won't enjoy reading it. Just write the good stuff from the beginning. If you're monofocally shippy to the point that, say, "the good stuff" doesn't start until after Snape and the Giant Squid have admitted their undeniably growing attraction for one another... well, you're very, very strange, but start there anyway. You can put in the explanation of how they got that way into little affectionate asides later on, and the story (though still most likely horrible) will be better for it.
Of course, this is an extreme example, but the general rule stands. If the story inspiration is a moment that burns in your brain and will not let go, and you're planning to write the events leading up to it just as a justification for how you got there - don't. Just start with the good stuff. Then keep going with the good stuff. When you run out of good stuff, seal it off and call it done. If this means that it comes across as nothing more than a series of pivotal moments in the lives of the characters, separated by spans of years in which relationships have grown and changed offstage, so be it. Toss in just enough information around the edges that the reader can figure out what's going on and run with it. It'll be a far better story than the one where both you and the reader suffer through the spans in between.
Of course, this is not universally true. In order to keep growing as a writer, eventually you have to deliberately push your own boundaries - but it's certainly a good place to begin.
There's another warning of how not to start...
There are a large number of fanfic authors, especially really shippy authors, who love to write about their favorite characters *being* together. That bit at the beginning where they *get* together is just a regrettable obstacle that you have to slog through to get to the good stuff. It's rushed, and poorly thought out, and poorly justified, and it shows. Don't give us the beginning that you have to get through to get to the good stuff. If you don't enjoy writing it, we won't enjoy reading it. Just write the good stuff from the beginning. If you're monofocally shippy to the point that, say, "the good stuff" doesn't start until after Snape and the Giant Squid have admitted their undeniably growing attraction for one another... well, you're very, very strange, but start there anyway. You can put in the explanation of how they got that way into little affectionate asides later on, and the story (though still most likely horrible) will be better for it.
Of course, this is an extreme example, but the general rule stands. If the story inspiration is a moment that burns in your brain and will not let go, and you're planning to write the events leading up to it just as a justification for how you got there - don't. Just start with the good stuff. Then keep going with the good stuff. When you run out of good stuff, seal it off and call it done. If this means that it comes across as nothing more than a series of pivotal moments in the lives of the characters, separated by spans of years in which relationships have grown and changed offstage, so be it. Toss in just enough information around the edges that the reader can figure out what's going on and run with it. It'll be a far better story than the one where both you and the reader suffer through the spans in between.
Of course, this is not universally true. In order to keep growing as a writer, eventually you have to deliberately push your own boundaries - but it's certainly a good place to begin.