Spending mana wisely is a simple yet vital skill, so here’s a quick guide that goes through the universal laws of mana conservation.
First off, no two heroes are alike, and you absolutely must get used to the mana usage of each of them independently, so that you can gauge how much to spam spells. What’s more, this article isn’t going to take into account things like Kassadin’s mana restoration on each auto-attack, or Cassiopeia’s reduced mana cost on successive spell casts, as that information is too highly specified. While the majority of these examples are framed in the context of a mid lane match-up, the principles hold true in all lanes. If you’re a jungler struggling with mana costs, only use your primary clearing skill when clearing camps (unless you have a blue buff), and you will find that your problems aren’t quite as bad as you thought ;).
Control The Wave; Control Your Mana
Early on, you don’t want to use your abilities on minions unless you have significantly stronger pushing power, or you need to clear a push faster. For example, if a Lux is facing a Ryze, using her E to push waves will force him to miss out on CS or use more mana than she did to get that CS, so it’s worth it for her to use abilities on minions as long as she follows up on those abilities, intentionally pushing the wave under tower. However, a Lux going against a Malzahar will have to clear quickly just to prevent being pushed. In other words, learn to focus down minions in a sequence that allows you to last hit them for farming purposes and only use abilities to push/prevent being pushed depending on the match-up.
Work Smarter, Not Harder
Let minions do your work for you. This goes along with the previous point in that, if you can be pushing, you want to. More minions means you have more protection from the enemy laner, and they have more threats to deal with. If you can build up a minion wave, your opponent must either use mana to clear it, or let it push under tower, lose farm, and make themselves more vulnerable to harassment.
Look for opportunities to have your cake and eat it too. If you are Lux, try to get Es off when you can hit multiple minions AND the champion, which means waiting for them to misstep. Simply put, you spend the same amount of mana while doing more with it. Any champion with an AoE ability can do this, whereas single target attackers such as Ryze simply can’t (until he hits 6).
The Deadly Art of Trading Efficiently
Auto attacks are highly underrated at low ELOs. Early auto attacks are very powerful even for AP champions, and are an essential form of harassment in lane. While this is obvious for characters such as Lux and Ziggs, it is true for champions that don’t have extra damage linked to their auto attacks. Even for someone like Morgana (with no special damage linked to her auto attacks) you have more potential Damage Per Second from your auto attacks during levels ~1-4 than you do from your abilities, and auto-attack damage remains significant long after these levels.
Avoid situations that will put you at 1% health and 90% mana. Don’t go in for a trade trying to get autos on them just because its mana-free damage (if you pay for harass with health you’re gonna have a bad time), make sure you can do so without taking damage, or that you will absolutely come out ahead in a trade. Among other things, this means remembering that minions will attack you based on the proximity of the enemy champion to their minions (not your proximity to their minions). If you lose a significant trade you have to use your abilities more defensively for awhile, which means you won’t be getting the most for your mana. As a rule of thumb, you want your mana and hp bars to be within 20% (of their max) of each other.
Use Those Abilities
Unless you are going all-in for a kill, it’s usually best to only use the most mana-efficient ability. This will be the ability that you put the most skill points in early, because the mana cost will go up slightly, but the damage will go up significantly (making it more mana efficient with each upgrade). Exceptions to this rule would be CC abilities on champions that get more from auto attacks, such as Darius. Using hook/slow combo will start stacking bleeds and allow you to get lots of autos off.
Maximize ability use. If you have a multi-target ability, you should probably be hitting multiple targets with it. Sona’s heal will always heal her +1, so if your ADC needs a heal and you are full health, go in for a trade (assuming it’s relatively safe) because you can essentially heal yourself for free. On the flipside, if you could use the heal, but your ADC is at full health, depending on the state of your mana it might be best to play passively behind them until they take some damage. Also, don’t use an ability (skillshots in particular) just because you have it; have confidence the shot will do something productive before you decide to invest in it.
Unless you have Kha’Zix or someone else that you know you can all-in with early, you usually don’t want to spend a ton of mana. Returning to the previous point, abilities get more mana-efficient with level, so don’t splurge with your mana until level 4-5 at least.
The Great Mana Item Question
Tear vs. Chalice vs. RoA. Every character is different, but in general, the MR and infinite mana from Chalice is handy for people you want to be trading/poking a lot with (usually having some form of sustain–a shield, heal, Spell Vamp, etc.) such as Lux and Nidalee. Tear is for people who benefit greatly from the stacks, and can stack it quickly, such as Ryze and Singed. RoA works very well with Tear on a lot of champions, but is often the sole sustain item for carries that don’t use tons of mana, but have low mana pools, such as Cho’Gath. You usually only want to get one of these items (Rod of Ages/Seraph’s on some champions being the most notable exception) but the most important thing in deciding which one to purchase is how it fits into the rest of your build.
As far as general rules that apply to any position, and any mana-using champion (AKA universal laws), I think that pretty much covers it. If you have more specific questions, I’ll be happy to address them in the comments. One way you can use this knowledge even more potently is by baiting your opponent into using their mana inefficiently. You’re laning against a Lux? Stay away from the minions so that you don’t let her get free harass on you. You’re laning against a Sona? Focus your harass only onto one person in the lane, so that she can’t use her heal efficiently. For every one of the above points outlining how to do things right, there is a way to do things wrong, and with the proper baiting and outsmarting, you can guide your opponents into misusing their mana, allowing you to make them dance as if they had a snake in their boot.
As always, I encourage you to ask, add, argue, etc. in the comments.