I believe the matchup is Marth 70:30 Link. I don't think it's as bad as Shiek, Falco, etc (those matchups are easily like 90:10 or 80:20 at least), but Marth is still pretty difficult to deal with so long as the Marth player knows what's up.
Link's main problem, as many have pointed out, is that he gets outranged by Marth in most moves and he's also slower in nearly every aspect. Basically, what Link aims to do is set up his Boomerang and Bombs to force Marth in an uncomfortable [sexual] position.
Good: Projectiles, Stage Control
For projectiles, they're Link's best tools: the Boomerang and Bombs are both very useful for stopping Marth's approach and keeping space. Mix up your bombs with your boomerang angles to restrict the space that Marth can approach you. Although Marth can deflect Link's boomerang and cut through bombs safely, he's still forced to make a move to cover himself from the projectile or get out of the way into a different position.
In other words, keep in mind that when you're zoning Marth, you should always throw your boomerang in angles that restrict Marth's approach options and punish the options he makes. Also remember that the boomerang comes back to you, so Marth has to shield, jump out of the way, dodge, etc. to avoid it. If the Marth player chooses to ignore the retreating 'rang, Marth will get spanked in the bum-bum by the returning boomerang, and he'll turn around [to see who touched him in an inappropriate manner].
Bad: Speed, Edge-guarded, Close Range
Always, always avoid situations where you're directly above Marth: this is not just Link advice, but advice in general when fighting against Marth. Link does have his bombs to control space when he's falling back down to the stage, but otherwise you should always avoid being on top of a platform where Marth is below. On the other hand, Marth doesn't like being above Link either, so keeping him afloat let's Link prepare Bombs, adjust your position, go at him with Up-airs, etc.
This matchup gets much more tricky when Marth gets close to you and when Link is off-stage, as he can really hammer the pressure on Link and edge-guard him really well. Most of your usual Out-of-Shield options (N-air, Up-B, etc) can be spaced properly by the Marth player and punish you for trying them. However, Link can still throw a Bomb OoS (if you have a bomb already) or Shield-grab most of Marth's moves (see Lootic's post). At low percentages, you can CC most of Marth's moves if he's trying to approach. I could go on and on about this, but there's already a lot of information in previous posts.
Counterpicking
It's tricky to give advice on counterpicking stages against Marth: much like how Marth's sword can hit through platforms with Up-tilt, Link can do the same thing to Marth on Yoshi's and Fountain, but Link covers less space. Also, since these are small stages, Link has a harder time keeping space between him and Marth. Personally, I like Pokémon Stadium, Dreamland and Fountain of Dreams vs Marth, but many Link players have different preferences: your friend will find out through more play which stages he likes vs Marth.
As for Jiggs, I actually think that's a better matchup for Link, I'd say that it's Jiggs 60:40 Link.
EDIT: I'm not a Link main, but he started as my secondary, and is currently the only other character besides Peach that I know how to play as. I originally picked up Link to play seriously in tournament sets vs. Jigglypuff and Samus. However, I have also used him seriously in tournament sets vs. Marth, C. Falcon, and Fox mains to see what happens, and I've actually won tournament sets with him. At GOML, I won vs. a Marth main after he defeated my Peach, and at a Kitchener local (Let's Play), I won a pools match vs. a Jigglypuff main who switched to Fox in the second game (I still won with Link). These results have satisfied me enough to keep using Link not just as a counterpick, but as a co-main with Peach.
