To properly equip a rune so as to cast magic spells with it, you need to have an item called "[Blank] Crystal" in your inventory(So, [Fire Crystal] or [Water Crystal]), and you need to pay a Rune Master to attach it to your character. If you're playing Suikoden 1, you haven't "equipped a fire rune to your weapon", you've attached a Fire Rune Piece (which is different from a Fire Crystal) which is going to give you bonus fire damage to your attack, not any magic spells whatsoever. There are also Rune Pieces that boost your stats, but those are obvious as they do not contain an element in their name (Power Rune Piece, for instance).
"Rune Pieces" are attached to weapons and grant bonuses in combat.
"Rune Crystals" are equipped at a Rune Master (Crystal Ball icon in towns) and give you spells/abilities.
It's a very important distinction, and it honestly isn't that hard to tell them apart if you read your item names/know which shop you equipped them at.
The whole system is a lot more understandable and useful in Suikoden 2, where they just tell you what it does and they use the same items for both purposes.
What were the best runes (edit: rune piece) anyway? I pretty much maxed my whole team with water because the healing each turn was pretty nice.
Fire and Lightning are pretty much interchangeable, each piece you attach gives you a small bonus elemental damage to your attack. I also understand that Earth fits here too, but I never really noticed a difference with what Earth pieces did. Wind Rune Pieces boost your defense, and Water gives you regeneration, as stated.
I always felt they were all underpowered and not really all that helpful, although I always stacked all my Fire Pieces on Viktor and Lightning on Flik, then piled Water on the Hero and Wind on Pahn or Pesmerga(Whoever I was using) with the last going on my Mage (Rubi/Cleo/Tengaar). That always worked out well for me.