How can I gather enough steel for smithing?
Solution 1:
You can craft steel ingots with Iron, Chalk, and Coal in an Ingot Press. Note that if your Tinkering (or Smithing) level is at least 1, this recipe produces 2 ingots for every 1 set of reagents, making Tinkering a very profitable skill tree to have if you need to produce Steel.
Iron ingots are pretty common, and don't forget that you can make them by pressing Hematite ore. Again, this is doubled if your Tinkering (or Smithing) level is at least one. Hematite and Iron are both fairly common. I had a stack of probably 50 Iron by the time I faced Dredmor. (Do note that Iron is also used to make Rust, which is an ingredient in certain useful potions.)
Chalk is fairly common, but can also be found by grinding Black Pearls. Combine this with the Piracy skill's ability to make enemies drop gems occasionally, and you should be up to your ears in chalk in no time.
Coal is a random drop, but it's also crazy common.
Finally, you can sometimes find Steel ingots randomly in the dungeon - there is one particular room that looks like a blacksmith's workshop that is almost guaranteed to contain at least 2 or 3 (sadly, random) ingots, along with other blacksmith/tinkerer crafting items. Sometimes you'll find these ingredients in crafting vending machines as well, or in the shop, so it pays to keep an eye out for these.
Solution 2:
There are a few options and considerations.
You get two of an ingot when smelting and you have any skill in tinkering or smithing. While many sources seem to show that this is a tinkering based skill, it is the max of either tinkering or smithing (so that tinker only and smith only both get two ingots while those who don't take either only get one). See the Dredmor Wiki on smelting for a bit more confirmation on this.
I will assume that you have smithing at this point if you are trying to make high tier items (trying to make them without the crafting skills would be challenging).
The key question then is finding the ingredients. Chalk can be obtained by grinding up black pearls. Coal just has to be found.
Finding the these materials can be improved with other skills. The perception skill is a bonanza when it comes to finding crafting materials. Lucky find can produce a steel ingot straight up - poof there it is. Luckier Find can produce coal and black pearls. Luckiest Find can produce more steel ingots. All of these Lucky Find skills can also produce varying qualities of weapons (For example, Luckiest Find can produce a steel sword - rather than needing 3x steel ingots to make it).
Specifically for improving finds of black pearls, piracy first level skill will randomly produce random gems - including the black pearl.
Clockwork Knight deserves an additional mention of its own. It is a skill that ties very well with crafting. In addition to giving boost to smithing and crafting as part of its skills (allowing access to the highest tier of crafting - for example Sword of Necropoking which requires level 7 smithing). This class has starting equipment of the tinkerer's goggles. The first level of Clockwork Knight has a skill that will activate 25% of the time to drop one of scrap iron, scrap steel, scrap copper, or scrap aluminum (50% chance to drop various other tinker things, and 10% chance to drop the more rare tinker things - but we aren't concerned with those here).
Some people play the game straight up with as few other changes as possible. Other people like to expand it a bit. If you are of the later type, the Steam Workshop for Dungeons of Dredmor has a number of mods (you can find many of these outside of Steam if you purchased it that way instead). The mod Advanced Craft'n'Smelt (non-steam source) includes a multitude of meltdown recipes for armor, weapons, and traps -- that steel axe that you just found that you don't use because you are a sword fighter, not an axe fighter... there's some steel ingots for you.