Do you have to add the "enchantment" cost to the weapon cost? Does the player just pay the amount? Do you have to buy a completely new weapon? For example for a +1 magic weapon, it costs 360... Is that the total cost for all weapons?
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There are two systems for items in 4e. The original system and the new system.
In the original system there were two ways to acquire magic items. You either found them while adventuring or you bought them from a shop. The rules on what was available from a shop were pretty thin and left completely up to the DM's discretion. The limiting factor here was that you could only use a Daily item power once per milestone (2 encounters) completed.
However, when Essentials came out, there was a change. They introduced item rarity and all magic items now have a rarity (common, uncommon and rare) and they removed the restrictions on daily item powers. You can get common items the following ways:
Rare and Uncommon items can only be found while adventuring (though some DMs will make an exception and allow you to purchase Uncommon items with strings attached. Our DM uses a waiting period for current or near current level uncommon items).
To answer your question explicitly, yes, the players just pay the amount listed on the item (for common items). However, this is an opportunity to bust out the roleplaying and have them find a shop, if you want they can haggle with the merchant (and maybe get a better deal! (just not too good)).
As far as the cost, this is dictated not by the enchantment level (the +1), but by the item's level, so all L1 items are 360 gold, all level 2 items are 520 gp.