Hello everyone and welcome to my analysis on Runes.
What I will mostly focus on in this article is Rune spreads and the reasonings for their usage. Here are the most common ones you'll find:

3 Speed: This is the most important Rune spread. All the monsters that run this spread have one thing in common: they have some crucial, almost always game-changing buff or debuff they want to apply on allies or enemies, respectively. The most common group of monsters to run this are deniers, who aim to stop all enemies from moving at the start of battle, and this obviously forces them to be as fast as possible. Another group is turn transferring monsters such as Rocigon and Samael forms, who aim to give an extra turn to one of their chosen allies, essentially making that target as fast as the turn giver - with this, the target can forgo Speed runes for more important statistics. Monsters that can disable traits such as Ingenica can also benefit from this spread to allow their deniers to deny without impediments such as Control immunity.

2 Strength 1 Speed: The classical attacker spread. This spread aims to maximize damage output by raising the Strength stat while preventing some opponents from moving twice before or after you. The Speed rune can be dropped for another Strength if you are sure that the power increase ensures that your monster will kill the target in a single hit. An alternative is to make it a Team Speed Rune instead, to fine tune your fast monster's Speed stat so that they outspeed the enemy's fast monster.

2 Life 1 Speed: A tank spread. This used to be the standard spread for tanks when they needed to move to apply their useful buffs themselves, on monsters like Ouros. Still a useful spread though. The Speed is usually dropped for another Life Rune for more longevity, since tanks don't care too much about being fast, especially in the case of Mega Taunt casters. It can be turned to a Team Speed Rune too.

3 Team Speed: Remember when I said 3 Speed was the most important Rune spread? Well, this one is a close second. This can be used on almost any monster you want since the goal is to speed up allies. Most of the time this will be paired with a 3 Speed monster, to make that monster even faster, usually to outspeed opposing deniers. An interesting thing about this Rune Spread is that one or two of the Team Speed Runes can be dropped in favor of Strength for attackers or Life for tanks, since it's enough to just outspeed your target - any more Speed is excess and takes from your valuable Strength and/or Life.

How to Rune?
Most monsters in the game will fit at least one of the Rune spreads given above, but sometimes one will have to get creative. Let's delve a bit deeper into this sandbox-ish Rune spread.
Some questions to be asked while Runing are the following:
-What am I trying to make my monster accomplish?
-What are the monsters on my team and the enemy team? How does my monster interact with the other five monsters on the field? What is the win condition of the two teams? How can I make the opponent's win condition fail, or mine succeed?
-What Relics do the other monsters have? Will they have a noticeable impact on what my monster is trying to do with the given Rune spread?
-If I want my monster to deal with a certain monster on the enemy team, how do the two monsters' Speed stats compare? Does it matter who's faster? Am I trying to one shot the target or prevent it from doing its job another way?
-Who has the fastest monster? How will I deal with getting denied? Can I adapt my Runes against this?
I cannot really list a singular, end all be all answer to all of these questions, but I will try to list the situations in which specific Runes are effective:
Life: Staying alive for longer. Tanking attacks.
Strength: Increasing damage output, possibly attempting to one-shot with a powerful move
Speed: Outspeeding enemies. Moving before all monsters or a specific monster.
Team Life: Making the team tankier. Ideal for drawing out the battle, if this is desirable.
Team Strength: Very very situational. If you were to use this, it is likely to try and wipe out the enemy team in a single hit, using it on a monster other than your attacker to pump up your attacker's power.
Team Speed: Making the team, or a specific monster on your team, faster. Trying to outspeed an enemy you normally couldn't with your given Rune spread.
With this, I hope I could give some insight on Runes. If you think I missed anything vital, feel free to tell me.