#1. PokeGnome[]
When trying to get this secret, just play normally, but there will occasionally be a gnome that runs out, tap him while playing casually and you will receive loot, but you will also get the easter egg as soon as you tap him.
#2. JukeboxHero[]
Very easy, start a smithery day, and tap the jukebox in the background once, changing the track, and giving you the JukeboxHero easter egg.
#3. Negotiate[]
After playing a round of Tap Smiths in the smithery, and it cuts to your squire selling it to the merchant, once all the money has been collected, just tap the merchant, which will play an animation of him taking a hit, and you will gain some more money, just tap him until you can't, and you will have the easter egg Negotiate, this is able to be done every day gone past.
#4. HiddenPage[]
Go to the informative section of the book, and click on the arrow to go to the end, after that, the page on the right goes blank, click in the area the arrow was in, if you got it correctly, you should unlock Grandpa Jeb and you should go to a page that looks like this: 
#5. SecretUpgrade[]
This one is simple, go to the upgrades page, and click to the Smithery Trade-In, click one more place to the right, and you should be greeted with a one level upgrade for 500 coins, called the Secret, the description reads:
This sigil increases the chance for Smith Specials to occur.
#6. SecretMenu[]
This one is very easy, but needs some instruction. From the main menu before going into the smithery, click into settings. There will be the settings, and Grandpa Jeb and Squire Smith on the two sides, tap on Grandpa Jeb once, Squire Smith twice and Grandpa Jeb once more, to get to the secret menu, this unlocks the Titan Smith, which looks like this: 
#7. Streak[]
One of the harder secrets, you have to get a streak of 40 in a Smithery day. It's good to have a lot of plat so when you can, buy some relics
#8. FoulBeast[]
This one is one of the more tedious achievements, you have to play for 365 in-game smithery days, this one will take some determination and hard work, but you'll make it. To celebrate this anniversary in game, Squire Smith will become a usable character, with a rodent special. Play one more round after this, and let the rodent attack the metal, once done, you will unlock FoulBeast
#9. IdleHands[]
This one is more simple, start up a smithery day, and don't tap. A gloved hand will appear and start tapping repeatedly to prompt you to tap, it appears to get faster as it urges you to tap, but just wait it out. As soon as a minute has gone by, start tapping the glove, you get IdleHands, simple.
#10. DuckDynasty[]
This one is a truly hard one to find, credits go to that one guy on the Tap Smiths official forum. Basically, you have to buy the shelf item "Rubber Ducky", then start up a game, and as soon as you're in, go to the shelf, and tap the rubber ducky, upon tapping it, you get DuckDynasty.
#11. Ninja Love[]
Equip the Ninja (relic) Assistant and NAME (#47) then start a day.
#12. PlayerTwo[]
This is one I couldn't have found without SmackTheZak from the TinyTitanStudios forum, thanks a lot!
Basically, you have to have the Fighter Smith unlocked. If unlocked, select the Fighter Smith on the RIGHT side, and then do the left side. You should unlock it when Player 2 is unlocked, and here is his appearance!: 
#13. ChooChoo[]
To get this Easter egg, you need the Flatscreen TV wall relic. Equip it and you'll see it on the top right of your smithery. There is a train on a railroad with a purple background. While you are playing a game of Tap Smiths, tap the TV to turn it off, and you will get the 13th Easter egg.