In most cases, you will do just as well on FD as any other stage by virtue of Marth's juggle. The exceptions to this (off the top of my head) are C. Falcon and Ganondorf: C. Falcon just does really well on FD, and Ganondorf actually just does better against Marth when there aren't platforms.
However, in many cases the approach game will be noticeably harder, as you will not have platforms as an avenue to avoid outsmarting your opponent. On FD, you won't have platforms to try and tech on, so any punishment will hit even harder. Keep this in mind, but don't let it lull you into thinking it's ok to use these things on stages where the punishment is less harsh.
General strategy is to try and bait, and to space aerials properly as an approach. Things like double-fair and non-fast-fallen (what a mouthful) aerials are canonically terrible, and will get you punished. These things should only be used for combos. Marth has a variety of safe options, and, in general, safe options are the ones which require the least commitment (and this is the reason Sheik seems so ****ing unfair to Marth; most of her moves have very little startup or ending lag, hence she doesn't really commit to anything). These moves are shffled fair, autocanceled nair (careful with this one, however) and dtilt. It is these commitment-less moves which you should primarily use for baiting.
Against most characters, you should also dash dance camp in order to bait. However, keep in mind that, against faster characters, you will need to do more. Dash dance camping is useless if Falcon just runs up and hits you and you can't run away in time. Solutions to this include pivoting (or simply turning around) fairs or nairs and pivoting fsmash.
Now, the above is not as important as what's to come: Marth does well on FD generally because of his juggle. In other words, while the approach is harder, in most cases he tends to get payed off a great deal more for successfully approaching. There are exceptions (Falcon being the most obvious one, and several are open for debate at the very least), but generally you should find yourself doing really disgusting juggle combos to your friends and family whenever they **** anything up.
Against Fox and Falco, you should memorize the chaingrab. At 0% you have to fthrow Falco, and he can buffer a roll (I think; I'll need to look into the frame data on this one), but afterwards you can proceed with standard uthrow fare. Against Fox you can start the uthrow chaingrab from 0%. At around 20% you will need to start pivoting grabs to do it successfully (if the opponent does not slight DI or try to shine you, it's not necessary, but do it anyway). At around 30% or so you need to start throwing in uairs and utilts. This entire paragraph could be off, however, so I wouldn't take it as absolute truth. Lots of players are much better at the chaingrab than I am, and to an extent you have to learn to do it through practice.
Against Sheik, I've summarized something of a strategy above. FD is unique in that her needles can screw with you a bit harder, but it's more than made up for by virtue of his juggle. Sheik can't do anything to Marth while being juggled because her only attacks to escape are nair and dair, neither of which hinders Marth's juggle in the least.
Against Falcon you should find yourself struggling a bit, but overall the matchup shouldn't be too much harder than on another neutral. You have to watch out for retreating nairs and dash dance camping, and in this regard Falcon really gives Marth a hard time. As far as juggling, it's about the same as anyone else, except Falcon has a dair which really makes Marth's juggle difficult to execute properly. On occasion (or frequently, depending on your juggling skill) you will get hit by Falcon's dair while juggling. Combine this with Falcon's falling speed and you realize that while juggling you need to be extremely attentive. Sometimes you will just have to accept that you have not uaired early enough and simply shield the forthcoming dair.
Ganon is a very straightforward matchup. Juggles work, but actually aren't necessary. Space your **** against him and you'll be fine. In a similar vein to Falcon, his dair can ruin your juggles, but his falling speed is so slow that it won't be an issue (although his dair has a larger hitbox, so you will need to learn the appropriate spacing).
For the remaining cast members, it suffices to apply strategies to the matchup and tweak them with the stage-specific information mentioned above. If there's anything else I can add, feel free to ask. And of course, if anyone sees an error in my post or disagrees with something, feel free to mention it.