From Diablo Wiki
It should be noted that the following explanation is taken from planetdiablo.com, which in turn took it from Venomous Vixen's Sorceress Guide. Also keep in mind that even though this explanation is centered on the sorceress, the concepts are true for all characters using mana.
How to affect the rate of mana regeneration
Your Sorc's ability to regen mana will be one of the primary factors limiting her effectiveness in combat, putting aside whatever personal ability you have when it comes to the arts of avoiding monster hits and using spells efficiently. If she cannot regen her mana fast enough, she will not have enough mana during combat, greatly increasing the likelihood that she will die. Thus, you need to work on improving her rate of mana regen. There are four main ways to do this:
(1) Add to max mana through the use of items
(2) Add to max mana through the investment of stat points into Energy
(3) Equip items that add specifically to mana regen rate
(4) Invest skill points into Warmth
There is also:
(5) Mana regen shrines and the Paladin's Meditation aura
(6) Skill shrines and the Barbarian's Battle Command war cry (if you already have Warmth)
(7) The Barbarian's Battle Orders war cry
(5)-(7) provide only a temporary benefit, or otherwise require that a party member use the skill in question. Because these sources of increased mana regen are unreliable, I will not discuss them further. Instead, I will now try to explain how (1)-(4) mutually work to improve your Sorc's mana regen ability.
The actual equation used in the game for calculating mana regen, in terms of mana per second, is this:
25 * [ [256 * MaxMana / 3000] * (100 + BaseRegenRateBonus) / 100] / 256
Where BaseRegenRateBonus = the sum of mana regen rate increases from Warmth and items. The brackets indicate downward rounding (i.e. what mathematicians refer to as "chopping", "truncating" or a "floor function"). Blizzard's Arreat Summit offers a simpler approximation of that formula:
MaxMana * ((100 + BaseRegenRateBonus) / 100) / 120
Which reduces to:
MaxaMana * (100 + BaseRegenRateBonus) / 12000
Obviously, the actual equation has more terms than you can shake a staff at; trying to use it to calculate your mana regen rate will be tedious and maybe even give you a headache if you do it enough times. The latter equations are much easier to use, although they will still require the services of a calculator.
As you would expect, adding to MaxMana independently of BaseRegenRateBonus will increase the amount of mana regenerated per second, and likewise, adding to BaseRegenRateBonus independently of MaxMana will increase the amount of mana regenerated per second.
Understanding Mana Regeneration
Mana regeneration can be usefully understood in terms of relative increases/decreases in mana regen rate. This way of thinking about mana regen is based on two empirical facts, which are the only ones you need to know in order to figure out how mana regen basically works, the above equations notwithstanding.
First - Adding to BaseRegenRateBonus does indeed make your mana orb refill at a faster rate. Items that add specifically to mana regeneration rate work the same way that Warmth does. So, you can think of them as adding "virtual" points to Warmth. Once you move beyond ~100 max mana, an empty mana orb will naturally refill in about 120 seconds. Assuming a base regen rate of 100%, increasing/decreasing that rate by X% will increase/decrease mana regen rate by X%. For example, doubling the base regen rate will double the rate of mana regen; an empty mana orb would refill in 60 seconds instead of 120. More concretely, if a Sorc had slvl 7 Warmth (+102% regen), this would give a regen rate of 202%, which is slightly more than double the base regen rate. That Sorc would be able to refill an empty mana orb in slightly less than 60 seconds.
Second - Increasing your max mana will also make your mana orb refill at a faster rate. For example, suppose you have a +N% regen bonus from Warmth and items. No matter how much you then add/subtract to/from your max mana, your empty mana orb would completely refill in about the same amount of time. But in order for that phenomenon to happen, the rate of regen must be further increased/decreased in direct proportion to how much more/less max mana you have gained/lost. So, increasing/decreasing your max mana by X% will increase/decrease your mana regen rate by X%. For example, if you were a starting Sorc (i.e. having 35 mana) who walked outside of town and found a cap that gives +7 mana, equipping it would not only increase your max mana by 20%, it would have the effect of increasing the rate at which you regen mana by 20% as well. Likewise, suppose you start out by leaving town and gaining your first level up. Adding 5 points to Energy would get you 12 more max mana (5 * 2, and the +2 bonus you get per level up), which would have the effect of increasing your rate of mana regen by 34%.
When I say that increasing mana by X% has the effect of increasing your rate of regen by X%, this is an approximation that is intended to be used in realistic situations in which you have to make a mana-related decision. There will be times when you feel that your Sorc is running out of mana too often and you need to do something about the problem. The solution may lie somewhere along (1)-(4), but it may not be clear which of those options will best solve your problem. Here is an example of how the approximation can be used. Suppose you have slvl 3 Warmth (i.e. +54%) and 200 max mana, not including your current helm which gives +20 mana. Should you get a gemmed helm? Well, equipping your current helm has the effect of adding 20 to max mana, which will increase mana regen rate by 10%. Suppose you have calculated that you can get +38% mana regen from a skull helm you are prepared to socket, and that a sapphire helm you are prepared to socket would give +48 mana. Which of the three helms is best, in terms of what it will do for your mana and mana regen ability? The sapphire helm would not only add 48 to max mana, but would also have the effect of increasing mana regen rate by ~24%. This clearly beats the magic helm. The skull helm would directly give (to BaseRegenRateBonus) +38% mana regen, which would be added to the (100 + 54)% regen rate already present to get 192%. But 192 / 154 = ~1.26, which is to say that your overall rate of mana regen would be increased by ~26%. So the sapphire helm and the skull helm would give basically the same increase in mana regen rate, with a slight advantage going to the skull helm. Which one you choose is a matter of personal preference, although either is better than the +20 mana helm. If your max mana had been higher, then the relative increase to max mana would have been smaller, and so, the skull helm would win by a wider margin, in terms of mana regen. If the skull helm contained skulls of lesser quality, then the relative increase to (100 + current BaseRegenRateBonus) would have been smaller; the sapphire helm would win.
This analysis of mana regeneration implies that in order to improve your mana regeneration ability, you should not only add to Warmth, but more importantly, you should increase your max mana by as much as you reasonably can by (1) adding to max mana through the use of items and (2) adding to max mana through the investment of stat points into Energy. Increasing max mana is the most efficient way to improve your mana situation, because not only do you have more mana to work with, but you will improve your regen rate as well. This is true independently of the mana regen rate bonus you get from (3) equipping items that add specifically to mana regen rate and (4) investing skill points into Warmth. Thus, increasing your mana regen rate by doing (3) and (4) will further improve the mana regen benefits of doing (1) and (2).