In order to evolve a weapon, or rather fusion two of them to a new one, they have to reach the max level (level 5). Once they reached the max level and you pick up a chest (from a boss or as a random drop), you get the evolution.
After the evolution you will be able to add another weapon to your repertoire, and, additionally, there is currently no limit for evolved weapons a player can have.

• Fire Staff + Frost Staff = Water Staff
  
• Frost Staff + Glacial Staff = Blizzard Wand
  
• Holy Bible + Thunder Staff = Raziel's Tome
  
• Holy Bible + Hellfire Staff = Underworld Tome
  
• Sacred Water + Hellfire Staff = Antichrist Blood
  
• Knife + Frost Scythe = Frost Dagger
  
• Knife + Frost Sword = Glacial Sword
  
• Celestial Sword + Ivy Staff = Horizon Sword
  
• Flame Crown + Corruption Robe = Agony Crown
  
• Flame Scythe + Frost Scythe = Obsidian Scythe
  
• Corruption Crow + Corruption Robe = Darkness Cloak
  
• Silver Gun + Snow Gun = Snow Cannon
  
• Corruption Orb + Slime Staff = Necrotic Orb
  
• Explosive Gift + Ectoplasm Wand = Ectoplasm Gift

If you find another combination, feel free to comment! :)