The usual way of getting Blue Essence
Blue Essence is a League of Legends currency that allows you - among other things - to buy champions, so they play an important role in the game, especially if you're going in a free-to-play route.
Buying champions with Blue Essence has slower progress than just buying everything in the game with Riot Points, the advantage of Blue Essence is that it won't make your wallet suffer.
The most common way of getting Blue Essence is through leveling up, but as you may know, the experience needed to level up will keep increasing from level 1 to 30, 30 to 50 and every 25 levels after, making you need more and more experience at each interval, so it becomes harder to get Blue Essence.
The first win of the day will give you 50 Blue Essence(as well as an experience bonus), so that is 350 Blue Essence a week if you win at least once each day, without considering the experience from the match. If you are under level 15 you don't have the first win of the day mission unlocked yet.
It can look very difficult to get Blue Essences if you compare the First Win of the Day reward with the price of a champion. Managing the Blue Essence you get is very important if you don't want to take money out of your wallet.
League of Legends will give you a lot of Blue Essence once you first start playing, and also champion shards, being the initial milestone rewards for levels 1 to 30, you will get Blue Essence and good random champion shards, if you are lucky, which you can use to buy the champions you like the most.
After each level, you will also keep getting more Champion Capsules that will give you shards or essences, and there are more milestones ahead, so it's not the end if you are already level 30 and wasted all your Blue Essence.
How do I refund League of Legends purchases?
You can refund purchases made in the League of Legends shop, this will allow you to get the currency spent back to your balance in case you regret what you bought. A very important note is that you only have 3 refunds available, so don't think you can keep refunding and buying things back, it doesn't work like that!
To refund a purchase, login into your League of Legends account in the desktop client, go to the shop and click on the little gear icon on the top right of the shop window, this will allow you to browse the purchases you made and refund them.
Although refunding can be a quick way to get some essences back to buy a champion you really want, you should avoid doing refunds for no reason, as you have a limited amount of allowed refunds and you may really need them at some point.
Get Blue Essence from events and missions
The game occasionally has events and those give you additional missions to complete, these missions often reward you with Blue Essences or some other currency currently in the game, most of the other essences can directly be used to buy Blue Essences or Champion Capsules, the capsules are more recommended because they can give you shards with a good Blue Essence disenchant value.
Remember to use your shards
Champion Shards can make you economize a lot of Blue Essence in the long run, or at least give you Blue Essences in case it is for a champion you don't really want, by disenchanting them in your loot tab.
There is no reason to keep your shards around if you don't plan to use them in the future, you can quickly disenchant them to stack up Blue Essence and buy what you really want.
It is also recommended to get Champion Capsules or tokens to possibly get shards, resulting in a higher amount of Blue Essences when comparing to buying them directly.
How to spend Riot Points wisely?
If your main focus is to increase the number of champions you have, or an overall higher loot than just buying what you want, you should take a look at event passes, they are your usual Battle Pass in any game, giving you more rewards as you level up after you buy them, getting a pass and progressing through it will give you a lot of some specific currency, which you can use to buy champion tokens or capsules if available, and also the pass own rewards, which aren't limited to just Blue Essences or champions, and can get you even skins.
It is what it is
There is no magic trick to get you champions and Blue Essence faster, the most effective way is playing the game(and trying to win) and taking a look at events to make sure you're not missing anything out, it is a slow process.
If you get an event pass occasionally, it will be a big boost to your Blue Essences and champions, while getting more for what you are paying.