Use some of the methods listed in the semi-guide below. Written by myself and Stormie.
Countess Running (Highest Rune = Lo)
Probably the most popular rune location. The countess can be found on the lowest level of the forgotten tower, in the black marsh. She has a special rune drop, so every time you kill her she will almost certainly drop at least one rune (1 in 64 chance she won't), and often up to 3. She is a favourite for rune upgrading (discussed later)
Although she can drop up to Lo, she can only drop up to Ist from her special rune drop - higher runes than that are not really any more common from her than any other boss.
The Hellforge Rush Technique (Highest Rune = Gul)
This one is time consuming. Offer to do free rushes to hell as long as you get the hellforge quest. Rush someone you find trustworthy (a forumer is the best bet) and complete the hellforge quest in act4. Consider whatever that drop may be your payment for the rush.
Hephasto the Armourer running (Highest Rune = Zod)
Hephasto the Armourer guards the hellforge found in the river of flame. Although there is no solid explication, I myself, along with some others, have found that Hephasto drops more runes that the average foe. You will have to kill him when hellforge rushing, but hephasto running includes killing him and only him (kind of like pindle running).
Running Level 82+ Areas (Highest Rune = Zod)
There are several level 82+ areas (full list of level 85 areas here). Each one has not only the ability to drop the highest rune, but they can drop a very good number of items. The level 85 areas can drop every last item in the game. The chances are very low you will find a rune, but if you MF in these areas anyways, a rune may show itself.
Farming & Upgrading
Farming involves collecting tons of lower-level runes. Upgrading (Ladder-Only for the high runes) involves transmuting two lower-level runes to a higher level rune by way of the horadric cube. The desperate will keep runes no lower than Amn, but most like to start upgrading runes at Lum or Ko.
Rune Upgrading recipies
Code:
3 Thul Runes + 1 Chipped Topaz = Amn Rune
3 Amn Runes + 1 Chipped Amethyst = Sol Rune
3 Sol Runes + 1 Chipped Sapphire = Shael Rune
3 Shael Runes + 1 Chipped Ruby = Dol Rune
* Below formulae are ladder only *
3 Dol Runes + 1 Chipped Emerald = Hel Rune
3 Hel Runes + 1 Chipped Diamond = Io Rune
3 Io Runes + 1 Flawed Topaz = Lum Rune
3 Lum Runes + 1 Flawed Amethyst = Ko Rune
3 Ko Runes + 1 Flawed Sapphire = Fal Rune
3 Fal Runes + 1 Flawed Ruby = Lem Rune
3 Lem Runes + 1 Flawed Emerald = Pul Rune
2 Pul Runes + 1 Flawed Diamond = Um Rune
2 Um Runes + 1 Topaz = Mal Rune
2 Mal Runes + 1 Amethyst = Ist Rune
2 Ist Runes + 1 Sapphire = Gul Rune
2 Gul Runes + 1 Ruby = Vex Rune
2 Vex Runes + 1 Emerald = Ohm Rune
2 Ohm Runes + 1 Diamond = Lo Rune
2 Lo Runes + 1 Flawless Topaz = Sur Rune
2 Sur Runes + 1 Flawless Amethyst = Ber Rune
2 Ber Runes + 1 Flawless Sapphire = Jah Rune
2 Jah Runes + 1 Flawless Ruby = Cham Rune
2 Cham Runes + 1 Flawless Emerald = Zod Rune
Other
Magic Find does not affect rune finding in anyway. Runes are purely luck, so if one does drop feel lucky.
As for other ways to get runes, just play though the game, runes pop up when you least expect them to.