Instructions
Open every crate you find and pick every lock you can. In addition to building up your lockpick skills, you̵7;ll find lots of gold ingots hidden in stashes throughout the game and from very early on. Gold ingots, like all of the items in Skyrim, are randomized in stashes, so playing through the game again and again won̵7;t reveal ingots in the same place -- except in a few key areas. The majority of ingots are found randomly throughout the game rather than these static locations.
Walk to the Forsaken Cave, starting either in Windhelm or Whiterun. Depending on how far along you are in the game, you may have discovered Forsaken Cave and it may appear as a place you can jump to on your map. If not, the easiest way to find it is to head east from Windhelm, staying north of Lake Yorgrim, a few minutes past the major fork in the road. It̵7;s east of the Nightgate Inn. Search the pot inside the entrance to find five gold ingots; two more are sitting on the table. The cave has a few serious enemies, including two frost trolls who may be difficult to defeat if your character is below level 15.
Warp or walk toward the Reach and discover Kolskeggr Mine. If you discover the mine as part of a miscellaneous quest from a peasant outside of Markarth, you̵7;ll have a harder time finding the ingots as the mine will be crawling with Forsworn. Instead, walk west of Markarth until you come to the river, then backtrack and head slightly north.
Enter the mine and use your pick axe to mine each of the gold veins you find in the mine. There are 17 ore veins, each of which will produce several gold ore. For every two pieces of ore you can use the smelter in any of the towns in Skyrim to make one gold ingot. Additionally, you̵7;ll find two formed ingots on the table with the briarheart near the back of the mine and two in a box in the back of the covered cart nearby.
Return to any city and find the smelter, then press the action button it to start it. Select any two gold ore from your inventory and then add them to the smelter, then press the action button to turn them into ingots.