How movement works

Have you ever given an unit a Special Troop just so that it can reach and capture a key city but after giving it, it still won't reach it? Have you ever given a troop a general so that it can start hitting since the very first turn but it falls 1 tile short in range? Have you upgraded a Special Force to get an extra movement point required to be able to disembark in that turn but after giving him that improved Special Troop, it still can only reach the port?

Well, worry no more! Now you'll be able to know if you should reach or how many movement points you're missing! I'm going to explain how movement works out in this last game of ET as there is no info provided by the game and it pretty much can be only known through testing.

Okey, first the basics. Every basic tile (those which show no picture when being selected) costs 2 movement to cross. Same goes for water tiles, crossing each water tile costs two. Now adding troops that are not affected by these, and to make them easier to spot, adding them in this order: infantry - artillery - tank and "Allied" troops in green while "Axis" ones in red, as it can help extrapolate (if someone wants) from what we currently have ingame:

Mountains: Parachute Regiment, Gebirgsjager - Maresal - Panzer. There are 2 types of mountains, the easiest way to differentiate them is checking how much defense bonus they give. The +1 costs 2 extra movement to traverse (making it 4 total), mountains offering +2 defense can only be crossed and used by infantry, but costing a huge 5 movement.

Jungles: ARR Airborne - SU 76M, M12 GMC - Yoshida, Chi Ri. There are 2 different forests, one that gives 1 bonus defense and costs 3 movement points and the other gives 2 bonus defense but costs 4 movement to go through. Snow covered trees (seen in Winter campaign) and cactus (in African campaign) are just skins, so it works the same way, check defense bonus.

Deserts: SAS - M7 Pries - no tank. These cost 3 to go through, both the ones giving +1 defense and the ones that don't.

Snow: White Death, L-39 Antitank - no art - no tank. These cost 3 movement.

Rivers: Irish Guards, Parachute Jaeger - no art - 44M TAS. These troops are also immune to the previous 4 special tiles mentioned above. These are the most painful to cross, costing a whopping 5. If there is a building over the river, then the river value will be the city value (see below).

Ground Buildings: a building costs 2 to capture it or move over it if it's already yours or from your ally. If its enemy building, it'll need an extra point of mobility (making it 3), with the exception of city centers (the ones that can train/recover infantry) that cost 2 extra, making it a total of 4. Ground oil refineries will not penalize movement at all, always costing 2 to capture or cross over, no matter if its enemy, yours or from an ally.

Ports: these are ideal places to embark or disembark quickly. Troops can just embark and disembark without suffering any penalization, however the port must be yours. If the port isn't yours, it'll cost 4 movement going over it instead of the usual 2, so capture it first before sending the rest of the troops so that they are not penalized and can reach further. Ports cost 4 movement to be captured, except it can easily be taken by combat ships (the 4 that are not transport ships) costing no bonus movement cost. 

Embarking/Disembarking without port: this one is as easy as your sister, troops must be on the tile next to the water (in case you want to embark) or to the ground (if you want to disembark). One the next turn, you will only be able to move a single tile into the other terrain, making coast embarks a slow method and easier to block

Lastly, combat ships can't move to where they can't see, so unlike other troops can go into Fog of war freely and reach its destination unless they collide with an enemy unit. Scouting first or sending in the cheapest ship (which has a high 4 vision) first will not hinder the movement of more heavy ships or ships that got their movement speed increased by a general.

But things get more complex as this is the first time ET added weather to the game. But worry not, because around 98% of the turns you play will be sunny, thus no alterations, but for that 2%, I'm letting you know:

Raining: every tile costs 1 extra mobility point to cross, even naval movement. (It also causes parachuting and air attacks/scouting to be impossible while it lasts)

Snowing: no effects to mobility, it causes morale to drop by 5 every turn and air operations can't be done

Hope it helps! I'll be polishing this guide and adding more if ET new versions do bring more troops, weather or tiles in.

EDIT 12th December: adding some extra tips:

Neither oil platforms in the sea (the one that grants +2 and the one with +4) cost extra movement to capture, they are the only exception to buildings, they will always cost 2.

Units will always be able to at least move one tile. If an artillery with 4 movement points is just next to a river, even though it costs 5 to go over the river, it'll still be able. Only exception is high mountains, that like mentioned before, can only be crossed by infantry, even if the artillery/tank Special Force has no movement penalization against mountains.

There is another movement altering tile, which seems like a Swamp, this one costs 4 movement to cross. Adding image as it's not that common and it'll help visualize it:

Adding examples of disembarking when a port is nearby, it should help visualize how it all goes.

In the first image, the armored car has 7 movement, so it can move once in the water (costs 2) and go in the port (costs 4), but it can't land as he only has 1 spare movement, when it needs 2 (as that tile is a plain).
On the second image I gave it Special Forces Prince Eugen, which raised his mobility by 1 point to 8. With this, it has two spare so it can even disembark and attack the city from ground.
On the last image, I sent another troop to capture the port. This will negate movement penalization for going over it, meaning the armored car now has 4 spare movement instead of 2 to move two tiles inland, making it ideal to be able to attack from another spot the city without suffering the transport ship combat penalization.