Could anyone help clarify how the three bars function. I understand that the middle one is in correlation to learning a new spell but I can't understand how the first and second relate to things, like which one relates to when I'm in the process of casting a spell, (I:E Guardian Spirit.)
I feel like I'm trying to hard to get this game and having such trouble grasping it. lol
Thanks <3

On the left, the Mana Bar shows how much of the mana you are "earning" that turn will be added to you Power Reserve.
The Power reserve is the mana you have to draw on when you cast a spell either from your tower or in combat.
(For most of my games I only have this bar set high for the first few turns, then set to 1 for the rest of the game unless I really need stock up on mana and do not have much gold to convert)

On the right, the Skill Bar shows how much of the mana "earning" that turn will be put into improving your casting skill. Casting skill determines how much mana you can spend in a turn. For example say your casting skill is 30 and the casting Skill Bar is set to give you 10 SP it would take 3 turns (30/10) to raise your skill to 31 then it would take 4 turns to increase your skill to 32 because you would now need to accumulate 31 points to increase the skill. So you should "micro" manage the skill bar.

The above does not take into consideration how some of the mage skills (Archmage, Channeler, etc) affect the learning rates, or the benefits you get from certain builds.

Joe's info about that "Mana" bar is right. It determines how much of the "Power" you earn each turn is turned into mana crystals for you to spend on spells and upkeep costs of certain spells like enchantments or Summoned Creatures like Magic/Guardian Spirits.

His comment about leaving it at 1 after the first turns is quite misleading though especially for newer players. You see this game has quite a few different ways to win and which you choose is the real way to decide how your bars will be set.

For example there is a thread here called "Let's Talk Summoner Builds" and with those you need lots of mana early so for the first, I would say 25~50 turns you would probably have your bar set all to mana so that you can summon your guys and cast the spells you need.

My favorite Build uses the "Retorts", aka Wizard Abilities that you pick, Artificer and Runemancer. This lets me create artifacts and get back double the mana I put into them. So I only get like 38 mana that I need to create my first artifact then I set my "Mana" Bar to 0 for the rest of the game usually.
This build also relies on the Heroes in game more than normal troops because you can make really super cool awesome Artifacts for them with kick but abilities like flying, magic Immunity, Guardian Wind etc. Read up on it in the Art & Rune thread.

The only bar you really need to "Micro manage" or watch often is the Research bar because all the others carry over so that no mana is actually wasted, however research does NOT do this. Therefore when researching say a spell that needs 20 research points you would want your research bar set at like 2,4,5 or 10 to not waste mana.

I am sorry to say that his info on the "SKILL" bar was wrong in how it increases, though close. Skill is short for Spell Casting Skill. This determines how much mana you can spend on spells during each battle as well as how long it takes you to cast spells with higher costs on the world map like summon spells, enchantments and Instant Spells.

Guardian Spirit for example Costs 80 Mana to summon. So if you had say a Spell Casting Skill of 20, it would take you 4 turns worth of your skill to summon one as long as you had the mana crystals to spend ofc .

In order to increase you Spell Casting Skill by 1 you have to spend twice your current spell skill.

In Joes example above to go from 30 to 31 would take 60 spent in "Skill". To then go from 31-32 would take 62. 32-33 would take 64 and so on.

The thing to keep in mind is that any "extra" carries over so if you say spent 75 mana to go from 30-31 then 15 would be carried over so you then only need 47 for the next one (62-15=47)

The "Archmage" ability you can choose is the only thing that can speed up increasing your skill. It basically adds 50% to any mana you spend in Skill so that it goes up faster. Also it gives a flat +10 Bonus to your casting skill at the end. For more info on that read the link below if you care about it.

masterofmagic.wikia.com/wiki/Spell_Skill

The far left slider is how much magic fuel you're buying. The far right slider increases the size of your magic gas tank.

Much of this has already been covered, and I'm kind of late to the party, but here's my version of the explanation.

The 3 sliders deal with how the magic power that you accumulate each turn is distributed. "Power" is generated by your wizard's tower (+1 per spell book you have, +5 if your fortress is on Myrror), by nodes you control, by religious buildings (shrine, temple, etc.), and by a few races (ex. high elves).

-The Mana slider acts sort of like your tax income, except for mana instead of gold. It pays maintenance for fantastic units (ex. sprites) and enchantments (whether unit or global). Any mana you generate beyond your maintenance costs is stored for later use. Any maintenance that isn't paid for by this slider will be paid from your mana reserve; if you run out of reserve then unfunded spells/creatures will be cancelled/disbanded.

-The Research slider, as you said, funds research. Research buildings (ex. Libraries) will have their bonuses reflected here, so if you have 2 libraries, then this slider will show 4 research even if you don't allocate any power here. As stated, any research for a turn that goes over what is needed to finish learning the current spell will be wasted; check in with your apprentice frequently.

-The Skill slider affects how quickly your spell skill grows. Your spell skill is how much mana (only from your reserve, NOT from your mana income!) you can put into casting spells overland each turn. It will take a wizard with 20 spell skill five turns to cast a 100 mana spell, while a wizard with 40 spell skill can cast it in three turns, and then the 40 skill wizard can still cast something that costs 20 mana on that third turn (or start another spell that is larger). In addition, you get your full allotment of spell skill to cast spells in each combat you participate; the higher your skill, the more spells and the larger the spells you can throw in combat. Each combat's allotment of spell skill is completely independent of each other combat and of overland casting. Fight three times in a turn, and you get your full spell skill for each. Note that all of this casting is just how much mana you are able to utilize each turn; you still have to actually have mana to cast anything.
Now, the Skill slider affects how quickly your spell skill grows. As EvilLoynis said, you need to gather 2x your current spell skill using this slider in order to add one point to your spell skill. Also as he said, spill over isn't wasted (usually). Sadly, there is no way to see how close you are to getting your next point of spell skill.
One caveat: You can only add 2 points to your spell skill each turn. The max amount to put into this slider is [4x+2], where x is your current spell skill. So if your spell skill is 20, there isn't any reason to allot more than 82 points into the Skill slider (anything more would be wasted). [Edit 1.1: This caveat isn't true. See Edit 1.2 for a little more detail.]

I'm much fuzzier on how retorts (wizard special abilities) specifically interact with these sliders, and whether the increases they provide are reflected in the numbers displayed on the sliders, so I won't go into that.

Edit 1.2: I just tested the spell skill cap last night, and I was wrong. There does not seem to be a hard cap on how much spell skill you can get in one turn; I was able to add more than 2 points to my skill both with Archmage and without it by pumping enough power into the "Skill" slider. This is using 1.31 (the version GOG sells).

From casual observation, the bonuses that add a % bonus to research/etc simply increase the number shown on the bar accordingly when you hit the correct threshold. IE: if you have a 10% bonus to research, the bar goes from 9 to 11 rather than 9 to 10. Those that reduce costs (such as Runemaster) instead reduce the total you need to accumulate.

When it comes to casting skill, one other thing is worth noting for a new player: any heroes you have that are also casters (with their own casting skill) will add half of that value to your own as long as they are stationed in your fortress city.