To answer this question, it is important to note that while humans can operate underwater, they prefer to do most things on land. We've been built by evolution to do best on land, and thus trying to work underwater usually turns out to put us at a disadvantage. This is probably going to be similar for merfolk; they're built for water, so doing anything on land is going to be hard for them. They may be able to invent things that help them survive on land, but at the end of the day they'll be glad to jump back into the oceans.
That said, the merfolk may find that there are some perks to working in the fresh air. For one thing, there isn't much resistance; this is bad for swimming, but good for things like weapons. Swords will swing faster, and arrows will fly further. I don't imagine the merfolk will have invented guns by this time, as guns tend not to work too well underwater, but to make up for this I'm sure they'll have many highly advanced underwater weapons that should work pretty well on land (and if they don't, like I said, bows are going to seem incredibly powerful to them without water resistance slowing down the projectiles).
Something that tends to not be as dangerous on land is explosives. If you're underwater and a grenade goes off next to you, even if you don't get hit by the schrapnel it's the shockwaves that'll do you in. On land, on the other hand, shockwaves in air don't do a whole lot. Based on this, it's plausible that merfolk won't deal too often with explosives on land. They just won't have the technology for it. If they discover fire, though, that's going to catch on like, well, wildfire. It's something that they can't use underwater, but is greatly effective on land (especially if they're deep-sea merfolk who aren't used to light).
From this, we have merfolk fighting with fire and simple projectile weapons (let's say crossbows). Now, as for where they'll fight and with what tactics, I'd say they will mainly be focused on getting back into water. As I said earlier, they aren't going to like being on land. But more than that, they probably can't even survive on land for too long. Humans breathe oxygen, and oxygen can be compressed to offer us a lot of air to breathe underwater; merfolk, on the other hand, breathe water, a mostly uncompressible liquid. Thus, their maximum water supply will be a fraction of our maximum air supply, especially since without water resistance anything the merfolk carry is going to feel a lot heavier than usual.
So I can see land combat revolving around bodies of water, with suited-up soldiers floundering on land from pond to pond, trading bolts and molotovs. Something similar to trench warfare may develop, as both sides build irrigation trenches through which they can swim. The no-man's-land will become the land, and anyone who tries to cross it will find themselves an easy target.