The word "resource" is used in two different ways by people talking about the game: sometimes people use it to say "food/hammers/commerce, and I don't care which," while sometimes people use it to say "the special squares that provide special benefits to a civ if the civ controls them and has improved them."
Let's only care about the first meaning for now: food/hammers/commerce (gold, in Civ terms, is something else than commerce).
Each tile produces "its" amount of food/hammers/commerce for a city whenever a "population point" from that city is using the tile. The tile can do that forever; it never "runs dry." A city has one population point for each point of size it is. For example, a size-one city has one pop point. You can tell where a city's pop points have been put to work by checking the city's city screen. (Later on, with some experience, you can also use the screen to overrule the computer's decision and set for yourself which tiles get worked.)
Okay, now the second meaning of resource. Some tiles are "resource tiles" and give special benefits to a civ that meets three conditions:
1) they control the tile (it's in their cultural boundaries)
2) the tile is improved (a worker has built the kind of "improvement" there that is appropriate for that resource, e.g. a farm for corn), and
3) there's a route to that tile: either a road leads to it, or it's riverside (or both, of course).
Resources in this sense also never go dry. Some examples of resource benefits are...
...extra health for every city with a connection via e.g. road and/or river to your capital
...extra happiness for every blah blah, or
...the ability to build certain units in every city with blah blah (e.g. no chariots without access to horses)
Can I move my units in any order I like?
Yes.
What types of movements are counted as turns?
Err... hum. I guess I would answer... All of them! I mean, there's no kind of movement that doesn't count and that doesn't cut into what you can do with the unit you moved for the rest of the turn -- it all eats up movement points. None of it's free.
(However, you can freely change your
build orders for your
cities as much as you want with no penalty. City orders switches are "free" and moves "not free" because city orders have no effect until after your turn ends anyway, whereas movement orders can have an immediate effect like starting a battle or revealing new information, so allowing "undo" here would be unfair.)
Now,
your turn overall ends when you click End Turn (the button at the bottom right that is green as long as you have some units that are not fortified/asleep and that still have movement points left, and turns red once you don't].
The turn for any of your units runs out when it runs out of movement points. Depending on where you move it and on tile improvements, it may move out of movement points right away, and it may not for dozens and dozens of tiles, because some units have more than one movement point, and entering some tiles costs less than (e.g. roads/railroads) or more than (e.g. unroaded forests) one movement point. SEE THE CIVILIPEDIA FOR DETAILS FOR INDIVIDUAL UNITS/TERRAIN TYPES.
In most cases, attacking also uses up all of a unit's movement points.
When
one of your units runs out of movement points, you can't use it again until
your next turn.
All clear?