Try to get to them when they are disembarking. Bombing and artillery are best, but even melee is still good.

I find naval bombers to be very effective. They're reasonably cheap to produce (plus are not limited to coastal cities to build), and can cover a large amount of ocean quickly. You can fan them out to search then bring them back to group them before going after whatever you find. They are the perfect pack hunters. In the late game you can even build them very quickly. Plus, cruisers are very underappreciated and naval bombers can often wreak havoc on ships.

In my last game, I needed to quickly transition from being a land power to a naval power and naval bombers served me well. I built three airports, queued a bunch of naval bombers at level one, and continued researching higher levels. I had to set my alarm for 2am to take advantage of the upgrade window to go from 1 to 3 efficiently, but that's the price you pay to play the game. I went from 0 to 15 level three naval bombers in 24 hours and had another three built and on hand when I needed them to go after a Pan Asian battleship stack that was foolishly deficient of cruisers or interceptors.

i agree, i usually mass-produce tons of naval bombers at my coastal, can bomb convoys, watch out for cruisers tho! i always have a stack of warships just incase.

Naval bombers are the best of course, if enemy dont have an hangar with Interceptors around. You can also use your fleet wisely by attacking with the correct unit and never exceed division size over 10 units to get the maximum firepower. For example i see many noobs that send loads of Battleships cause they think they are the best. Few subs on them and they are gone. I use Destroyers and subs alone in sets of 10 units to be able control them individually and maybe 6 BS with 2 destroyeras and 2 subs just incase.

Destroyers kill subs
Subs kill Battleships
Battleships best against landobjects and other Battleships
Cruisers kill planes

You also get the benefit of speed if you let Destroyers and Subs work on their own.

i meant warships as in destroyers,cruisers and battleships. not just battleships.

Use any ranged units (arty, ra, spra) you can get your hands on.
If you have a stack of naval bombers (which I try to have at least 1 of at all times) - use it on any disembarking troops
If the land troops have disembarked, use tac/attack bombers to deal serious damage
If the enemy is using air units from air carriers, use interceptors to defeat them.

For sure try to kill the enemy transports before they finish disembarking.
The units will get much better attack, defense, and hit point value after the land.
You definitely want to kill them before that happens.

How to do that, you can see above: Bring artillery if you have it, use bombers (especially naval) but any bomber works in a pinch because transports are so weak against air attack.

In case you're wondering: Yes, it is better to use a land attack bomber against a transport than to wait for the transport to become a land unit.

If the enemy has air cover, then you have to be more careful. If he has interceptors, then bombers will have a hard time, so you have to fight his interceptors with yours first. If the enemy mostly brought bombers, then watch out for your artillery, either stack them with AA or patrol with your interceptors or keep them out of range. If the enemy air force on his carriers is more powerful than your air force, and he's landing an army on your shore... then you're basically done

Look at their HP and Damage Potential. Act accordingly.

You mentioned they had a variety of ships. I'll add, because no one else has (and it didn't occur to me the first time). If they have battleships, be careful, they will outrange any arty you have with the exception of railroad guns. A smart player will typically send any ships capable of bombarding across your coast to ensure no defenders exist to oppose their amphibious landing.

I am currently preparing for this, and have done so before quite frequently (see Coast Defence)

Long-term preparations (within forseeable future) (You may not have time to do this):
If potential enemies are across large ocean, capture islands in the middle. Like a halberd, you can use them to hold the enemy advance at bay, or to thrust forward at him. Fortify these and base large warships there. That way, you can intercept fleets setting out. Build airstrips and use naval bombers to monitor shipping activity.

Medium-term (within 48 hours):
Send any fleet capacity you have to intercept invasion force. Most people won't bring huge numbers of fighting ships along with transports, and if they do, they'll be vulnerable. Take out especially his carriers, since you'll then have air superiority to destroy his fleet, and he will be powerless to stop you.
Fortify coastline if you think you can.
Build lots of artillery, both rocket and gun. Put artillery in coastal forts with anti-air if he has carriers. Use these to destroy disembarking troops.
Build submarines and naval bombers (and even rocket-bombs, as they're cheap and effective en masse)
Collect any submarines or naval bombers you have to destroy transports.
Move capitol if you can. Fortify it.

Short-term (within 12 hours)
Build submarines.
Collect any submarines or naval bombers you have to destroy transports.
Spam militia or anti-tank to slow him down, as well as building artillery. Put artillery behind your cannon fodder.