Blacksmiths are used to craft equip for your pets. Equip can be used to help advance in dungeons, to craft better gear (hammers), to help alchemists (pots), or to make adventurers stronger (sticks). Equip also provides stat bonuses. Equip is generally necessary to progress into Depth 2 dungeons and beyond.
Blacksmiths craft faster and with better quality as they reach higher Class Levels. They gain experience by crafting or by being in dungeons. They gain experience in dungeons just like any other pet would, but for crafting there is a different formula. 250 * (1 + growth / 20000) * (hours crafting) * (1 + crafter speed / 100)
The first blacksmith that is relatively easy to evolve is Hermit Crab. It is recommended to also evolve a wildcard pet, such as Bug or Mouse, to a blacksmith. You will generally want to have 1-2 blacksmiths early on and then get more as you go. If you have a pet with a blacksmith bonus, there is no reason not to make it a blacksmith.
Deciding on What to Craft (Blacksmith)
Once you have your blacksmith, the next step is deciding what you need to craft. In general, you always want your blacksmiths to craft something, so the first thing you should consider is creating a hammer to improve their crafting.
Progressing a blacksmith hammer to T2 SSS+20 should be an eventual long-term goal. With this hammer, all your odds of crafting gear with a good modifier increase. Your crafting speed also improves, meaning you can craft more faster. Both of these combine make putting a quality blacksmith hammer as a priority. However, you shouldn't be burning every single resource you have trying to get the perfect hammer. If you end up with a T2 A or S hammer, you should consider taking one of those to +20 to avoid spending everything finding the perfect hammer.
It is also recommended that you create 2 of these T2 SSS+20 hammers before attempting to move into T3 since one hammer will be used by the pet to boost your speed and quality while the other will be transformed into a T3. However, moving into T3 can be incredibly expensive and early on it can do more harm than good as you will have a much higher chance to create a very low Tier until your blacksmiths are a higher Class Level.
In general, you want to craft any t1 equipment and get them to +5 or +6. Once you do, you use it to craft the t2 version. If the t2 version is B or lower, you should consider either holding it as filler gear or scrapping it. This is a much better option vs. spending resources to improve their rating. The only time you do this if they are S or SS and you have a lot of resources invested into them. At that point, raising their rating is significant and worth the cost.
Beyond the hammer, you should target the gear your pet needs. It should have been mentioned in another guide, but you generally craft the gear that optimizes your pets. Mages tend to get fire swords, Assassins and Rogues get either a fire sword or knives, and armor/accessories of their element. Defenders usually get a pot or iron sword and Neutral armor/accessory. Supporters tend to get fire swords or knives and either their same element armor/accessory or more defensive iron armor. Equipment needs change based on dungeon, pet, and dungeon depth. For more information, check out this page: Equip and the Dungeon guide by Malfat Dungeon Guide
This should take a majority of your blacksmith's time. If you find yourself in a position that you aren't using them (lack of resources), then focus on crafting the Nothing item (these are very useful for Santa and Mimic. Better gear nets better dungeons which nets more materials. You can turn to the alchemist guide to learn more about their role in getting resources you need.
As you get farther into the game, you will notice that some of your blacksmiths have higher forging chances than others. You should use these blacksmiths to forge new equip, and the other blacksmiths should focus on reforging or upgrading.
For an in detail look at equipment you can craft as well as their stats and costs for upgrading/reforging, check out this section : Equipment Crafting
Alchemists are used to craft items that help with dungeon success. They are critically important for progressing into further dungeon depths and crafting the materials needed to evolve pets. Wildcard pets often end up as alchemists.
Alchemists are able to craft faster at higher Class Levels. They are only able to gain Class experience by crafting (except for the Stale Tortilla/Taco pet, which is unique). The formula for exp gain is 250 * (1 + growth / 20000) * (hours crafting) * (1 + crafter speed / 100)
Selecting Your Alchemist
Early on, there are a few easy choices to make into an alchemist. The first one is Bee, which is obtainable after you beat Diana.
If you are further on, than a few more alchemist pets open up. Bug and Camel are both wildcards (See Pets) that can make decent options for Alchemists, even though they don't have an alchemist class bonus. Beyond that, there's a series of token pets that you can evolve to alchemists, such as Question, and Rose.
As you unlock more and more pets, and get deeper into the dungeons, you'll start to get many more Dungeon supplies and items you can use for Crafting, as well as a desire to create talismans or rebirth bacon. As such, the need for more alchemists starts raising pretty fast. A token on a new alchemist is never wasted.
Deciding on What to Craft (Alchemist)
When you're starting out, you may not have the resources to do much with alchemists. The good thing is that there will always be something to craft.
Ideally, you are using alchemist to craft T2 materials to help you evolve your other pets or create T1-T2 gear. Early on, you will mainly be finding T1 materials, with a few T2s here and there. The ability to sustain constant blacksmith crafting is often determined by your alchemist's ability to create the materials.
Another option is to create items to help with dungeons. Generally, it's recommended to not craft the event-specific items (like flying boots) early on. You should buy those instead. What you can be crafting is items you can't buy in the store, like antidotes or health potions. These items can help you push your difficulty further. However, you should avoid depending on these items, as you can burn through resources that could be better spent elsewhere. Instead, use them if you are trying to push a dungeon and see if your team is ready for it without health potions.
If you have nothing to craft, then you can craft the item "Nothing". This is an item that originally served no purpose. The Santa pet can now be traded "Nothing" for 1-6 (depending on class level) Chocolate each. It can also be used later to spawn the Mimic enemy in dungeons.
For a more detailed look at things you can create and a simplified list of their costs/usage, check out this page : Items/Materials