Chronos: Before the Ashes

Enemies will sometimes drop Dragon Shards. You use these to upgrade weapons. If you have the hint system enabled as you begin the game, it will tell you exactly what to do. You can also find a Dragon Shard inside a Dragon Inscribed Box, which you can find pretty early on in the game. Check your inventory when you find it, and examine to open it for another achievement (Hidden Treasure). I'll explain where to find that in a separate guide.

You need 3 shards for your first upgrade if you are using a sword. Unsure if that's different with the alternate starting weapon. Comment if it is and I'll add to this guide.

Once you have enough shards, open your inventory and select your weapon. Then press X to upgrade. Easy peasy.

Just so you know before going crazy upgrading stuff - unless you plan on grinding materials, you will only be able to max out one or two weapons on a typical playthrough, so choose wisely (I liked playing with the mace - the weapon you can get after defeating the golem). The max is +5, however there is a trait available at a certain age to go to +6. I do not remember which age it is exactly, but I do know it is one of the second half traits (age 40-80). My advice is to only upgrade to +2 until you have a weapon you really like (aside from your starting weapon, there are 3 you can get before traveling to the second world and the spear is available in the second world). The last weapons you can get are late in the game, so save up your shards if you want to use one of those towards the end. As I mentioned before, I liked using the mace for most of the game. On my heroic run I ended up maxing the Krell sword (found just before entering the Labyrinth), and using that to finish the game.