There are multiple ways to get across water and to shift between planes.
For getting across water the simplest way is to build a boat (in a coastal town) and move your troops onto it. The types of boats you can build are determined by what race the town building the boat is. You can also summon a Floating Island (Sorcery) that acts like a boat. The other primary method is unit enchantments- Water Walking (Nature), Flight (Sorcery), and Wind Walking (sorcery) will allow units to move freely over water. Flying units can also move freely over water, along with Lizard Men units. Also, if you control a city on the other side of the ocean you want to cross you can set up an Earth Gate (Nature) in that city and another city, allowing units to move instantly between the cities.
For moving between planes the simplest way is to move units onto wizard towers (green towers on the map) then toggle between planes. You can also use the unit enchantment Planar Travel (Life) to allow a single unit to move freely between planes, or the spell Plane Shift (Life) to instantly move all units on a square between planes. Additionally, you can cast Astral Gate (Life) on some of your towns, allowing units stationed in those towns to move freely across planes.