Your Clvl and the difficulty level of the quest reward has nothing to do with the number of sockets you get. The number of sockets from the socket quest is not affected by the difficulty level, only by the ilvl of the item, which is based on the mlvl of the monster that drops it. Check the master table below, or the individual Armor and Weapons pages for info on how many sockets are possible on given item types. This limitation only applies to sockets that are spawn naturally, not ones which are added through the cube recipe or socket quest. Items can only naturally spawn with a maximum of 3 sockets on normal difficulty, 4 sockets on nightmare and 6 sockets on hell. How many a given item can get is random for most item types, but the maximum is always limited by the mlvl of the monster that drops the item, item type and in the case of naturally spawning sockets the difficulty level. It follows the normal rules for the generation of magical items, see the Item Generation Tutorial for details. The issue of possible affixes (or bonuses to single skills on wands, orbs etc.) is beyond the scope of this article. Weapons which cannot have sockets (like throwing weapons) won't get any socket and those with a maximum of 1 socket (like a few daggers and wands) have no chance for two of them. This results in a magical, socketed weapon that can be rerolled again with chipped, normal or flawless gems as many times as desired.
This doesn't add sockets to the existing weapon though, since it is rolling new mods on the weapon, so is essentially random. The only partial exception is the 3 chipped gems + 1 magical weapon recipe, which will create a magical weapon with new properties and 1-2 sockets. You can never add a socket to an item that already has one or more sockets, with any recipe or the socketing quest reward. Also items can generate with a variable number of sockets, and how many depends on the monster that drops them, the item type, and much more. There are three Cube recipes to add them, as well as the socket quest in Act V.
Socketed Items can be complicated, mainly in the number of sockets and how to add sockets to existing items. 6 How to Obtain Socketed/Socketable Items.