It does help if you mention which game you want to level up the weapons on, as most games have different leveling systems. In general, you must defeat enemies to gain a type of experience, which accumulates on your weapon. Once your weapon has enough experience, it goes to the next stage/level.
In some games, a weapon's attributes must be built up to access different stages of a weapon's upgrade path. These can be improved by leveling up the weapon in question, with the attributes improving each level, or by combining the weapon with some type of item either bought, found, or dropped by enemies. Sometimes, you must level the weapon up to get a form of upgrade point before you can combine items. Different items usually increase different attributes by different amounts.
In some games, a certain enemy/ type of enemy must be defeated with the current weapon to access the higher stages of the weapons upgrade path. This requirement is set so that you can't build your weapons up to legendary proportions at the start of the game (due to the fact these set enemies will only lurk in the bowels of the later dungeons) and therefore cut a swathe through anything in your path and breeze through the rest of the game
Finally, some weapons in some games can only be either bought, made, requested for a merchant to make the weapon using some of your own supplies and money, found or achieved by matching certain completion conditions. Also, some games require you to level up the characters, and the weapons don't change.
Unfortunately, this is all the help I can give you until you rephrase this question, saying which game it is in.
In Final Fantasy XIII,go to a save point,select upgrade,then select the weapon or accesessory to make stronger.