How can I change the number of sockets for Runewords?

No. An item with sockets has exactly that many sockets forever, and it cannot be altered.

You can give white items to Larzuk in Act 5 once per difficulty as a quest reward in order to have him add sockets to the item. The number of sockets added is based on the specific item you're adding sockets to (it will always get the maximum for an item of that type). If you add sockets to a colored item this way, you will get fewer sockets. Most colored items only give 1 socket, although blue (magic) items will randomly give 1 or 2 sockets.

Once an item has sockets, you can not add additional sockets, or remove any. However, if you have a white item (armor or weapon with no sockets in it), you can add a random amount of sockets to it via Horadric Cube recipes. As bummzack pointed out below, the odds for getting a certain amount of slots via recipe isn't always equally distributed. The game rolls a random number from 1-6 to determine how many sockets will be added, but if for example the item you have can only have a maximum of 3 sockets, there is a 1/6 chance of adding 1 socket, 1/6 chance of adding 2 sockets, and a 4/6 chance of adding 3 sockets (rolling anything from 3-6 will result in 3 sockets).

You can also use your Act 5 Quest 1 reward at Larzuk to add slots. The number of slots added will vary depending on the type of your item.

• Magic Item (Blue) = Random 1 or 2 slots
• Rare Item (Yellow) = 1 Slot
• Set Item (Green) = 1 Slot
• Unique Item (Gold) = 1 Slot
• Normal/Exceptional/Elite Item (White) = Max # Slots item allows for (not always 6, varies by quality and item type so look this up before socketing!).

Note that in your case, only the white quality above matters as you can only put Runewords in white items.

Yes and No

You cannot add sockets to or remove sockets from an item that already has sockets, but you can add sockets to unsocketed items.

There are two main ways to socket white items: the Horodric cube, and Larzuk's quest reward. Both require unsocketed items. The Horodric Cube recipes only work for non-superior items, which makes superior items with less than max sockets valuable, if they have the correct number for a popular item.

Socketing Items at Larzuk

Larzuk is occasionally, if infrequently, a good choice for socketing a white item. He'll give it the maximum number of sockets it can have, which depends on item type and item level (which is hidden, but can be inferred if you know what monster dropped the item).

The usefulness of that is limited, since you can only socket three items per character at Larzuk (one per difficulty as a quest reward), and it's more common for items to need less than max sockets to reach their true potential: 3 socket armor is much more valuable than four socket armor, because most of the good armor rune words use 3 sockets, and four sockets is much easier to find.

Larzuk is the only way to add sockets to superior white items, however, so there are a few cases when it's worthwhile to spend your Larzuk socket on a white item, instead of saving it for an otherwise unsocketable set or unique item.

Horodric Cube Socketing Recipies for White Items

These work only for non-superior, non-low-quality white items.

1 Tal Rune + 1 Thul Rune + 1 Perfect Topaz + Normal Body Armor
=> Socketed Body Armor of same type

1 Ral Rune + 1 Amn Rune + 1 Perfect Amethyst + Normal Weapon
=> Socketed Weapon of same type

1 Ral Rune + 1 Thul Rune + 1 Perfect Sapphire + Normal Helm
=> Socketed Helm of same type

1 Tal Rune + 1 Amn Rune + 1 Perfect Ruby + Normal Shield 
=> Socketed Shield of same type

The number of sockets is chosen randomly between 1 and the max for the item type (4 for body armor, 6 for weapons, 3 for helms, 4 for shields), and then capped at the max for the specific item, based on type and ilvl.

So, for example, a crystal sword dropped in Normal difficulty act 2, capped at 3 sockets by ilvl, will get three sockets 4/6ths of the time, two sockets 1/6th of the time, and 1 socket 1/6th of the tie, while a high level circlet will get one, two or three sockets with equal probability, because the maximum number of sockets for a helm is 3, while the maximum number of sockets for a weapon is 6.

source: Arreat Summit: Horodric Cube