How do I acquire the necessary requirements for this? I chose a Rogue with bow in the beginning and I'm still level 1 because I kind of have to avoid dungeons as I have miss too many times in darkness. I found the scroll in some chest I managed to steal in the first village.

Cat's Eye is a Divination spell, so you'll need a couple of points of Divination. The more points you put in Divination, the higher level you'll be able to use. I think it lasts for 40 rounds per level?

And I can choose Divination next level or does that skill require something as well?

FYI, if you don't put too many points into divination spells, you can get a better version of cats eyes in arcane/mage spell tree. You can train to get the points so your not spending/wasting points. It has a different name but in book 1, this spell is better than the priest one by 20% chance to hit. I dont remember where I read it, but i think it was the thread on book 1 and melee/buffing spells. One of the users proved that cats eyes is good in beginning but once you get the other, is pointless. The 2nd town should have it. Hope this helps.

Ah, thanks. I wonder if I can bear it without fighting in dungeons without it until 2nd town though.

I was running out of options so I bought 2 Cat's Eye potions because I had 500 xp until level 2 and it took forever with only 8 xp per Salamander. I managed to kill all in the dungeon to get the key from Leurik but I'm level 2 now with Cat's Eye as a spell but it's very weak, the light only reaches 2 squares away from me and now I'm out of gold so I can't buy any arrows and deal very low damage and hit almost never in melee with either hands or my dagger.

I entered the Cemetery now but the bats are too strong. Am I supposed to miss this much? I've 21 in Dexteiry and Concentration yet it seems like I usually have only 50 to 65% hit rate with my bow. I might have spread my characters to thin with too many skills in the beginning at level 1 instead of maximizing my bow and stealth as I noticed in the beginning that I could hit enemies even during stealth. I'm thinking of restarting but I think I'll try another class.

There are three low level sight spells to consider.

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Cat's Eye (Divine) - In order to cast this spell you need at least one rank in Divine Magic (inaccurately called Divination). This means starting as a Healer (which gets it free), spending three points to buy the first rank, or finding an NPC who will train you in the skill.

On its own this spell gives terrible illumination. It's akin to low-light vision from D&D. By itself you can barely see the walls next to you, and as such seems fairly useless at first blush. Where this spell is useful is in conjunction with another light source, like a torch. Since it grants low-light vision, it will extend the vision from another light source even further, stacking with that illumination.

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Gravedigger's Flame (Arcane) - In order to cast this spell you need at least one rank in Arcane. This means starting as a Mage (which gets it free), spending three points to buy the first rank, or finding an NPC who will train you in the skill.

This gives you hands-free light, so is good for two-handed characters like archers. It will illuminate your area, but also lets enemies see your position and draws them to you.

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Predator's Sight (Arcane) - In order to cast this spell you need at least one rank in Arcane. This means starting as a Mage (which gets it free), spending three points to buy the first rank, or finding an NPC who will train you in the skill.

This spell essentially gives you infravision, causing all enemies nearby to glow green. This eliminates darkness penalties when attacking and has the benefit of NOT illuminating you. Thus, you can attack while stealthed, or at least leave them to suffer darkness penalties to hit while you don't.

Predator's Sight looks something I could make use of. Is there a trainer for Arcane somewhere and if so, where? Also, the scroll of the spell. Are all items randomized everywhere in this game (chests, traders)? I've never liked that because then I'll have to reload to get what I want and I reload enough as it is.

Both magic schools you can train in Blackwater. (You need to sneak past raptor swarm, I did this with Hide in shadows level 6 during night). Level 5 in Elemental is enough for level 3 spell, 120 rounds duration.

Randomization - some items are preplaced, some randomized.

Scroll I got in Blackwater from trader by reloading.

Cat's Eyes > Predator's Sight

It gives you some illumination compared to Predator's sight none and it also negates the darkness penalty. I use Gravedigger's Flame instead of a torch and Cat's Eye for combat in the dark.

You can use minimap instead of illumination.

Upon digging on basilisk forum I stumbled upon "Predator's Sight > Cat's Eyes by math". I think this is based on difference in mechanic - Predator's sight removes penalty on fight in darkness, Cat's eyes extends vision range. For bowman PS is better.

Using minimap instead of light source is just silly, you'll miss all the levers and containers.

Like I said, Cat's Eyes also removes darkness penalty. I just recently beat Whistling Cave using it and I had about 60% hit chance while drones had about 20%. Also, you can just press TAB to highlight any nearby enemies more or less the same way as Predator's Sight does.

Not really, this is based on level of Cartography.
http://www.basiliskgames.com/forums/viewtopic.php?f=3&t=1555
7 "free levels" is enough to navigate.

So does Predator's Sight make it physically easier for ME to see where I'm going/where I'm stepping?

Predators Sight just makes enemies glow green.

Cats Eyes illuminates one square around you

Gravediggers lights up more but enemies can see/ target you easier