This is the current Bolt Thrower deck I've been using with some notes on card choices and how to play it.
3 Innovation
2 High Elf's Disdain
2 Wake The Mountain
2 Pilgrimage
1 Judgement of Verena
3 Master Rune of Valaya
3 Flames of the Phoenix
3 Gifts of Aenerion
3 Reap Whats Sown
-- 22
3 Warpstone Excavation
3 Contested Village
3 Keystone Forge
3 Dwarf/High Elf Alliance
3 City Gates
3 Treasure Vaults
3 Repeater Bolt Thrower
1 Temple of Vaul
3 Contested Stronghold
3 Abandoned Mine
-- 28
I hate this deck. But it's really very good. Non-rush decks have very little chance in the current tournament environments where sideboards are not allowed. The only real way for them to win is for you to get a really bad draw (e.g. multiple Flames of the Phoenix in the bottom few cards of the deck) and you losing to your own deck. That kind of thing does happen with this deck, but it's possible to mitigate that quite a bit by playing correctly. It is not a forgiving deck and it is very easy to lose by misplaying a development and so on, so if you want to play this in a tournament I would advise you to get as much practice as you can.
Unfortunately, the worst matchups for this deck are the other strongest decks in the environment right now - Orc/Skaven and DE/Skaven. Most of the DE/Skaven decks cannot run Pillage without giving up equity against other matchups, so usually scouts are the worry there. Good use of developments and Abandoned Mine is usually enough but sometimes they will get lucky. Other times they will just get a good Skaven draw, e.g. first turn Greyseer to Kingdom, 2nd turn 2x Elite, attack for 8 and that will beat you too. The Orcs have a much faster start and can Pillage an early Stronghold or Mine, so they probably have the best matchup. In a magical Christmasland where you have sideboards they are definitely favoured because they can run free Mob Up!
Alright, down to some card choices and play notes. You need Disdain for sure because otherwise you can run into problems in some matchups, e.g. against HE/Dwarf that can Disdain your Flames and has toughness units. It's also useful to counter Pillage & Demolition on your key supports, especially Abandoned Mine and Contested Stronghold. Opponents that save support removal for your Bolt Throwers will usually lose. Smash-Go-Boom! would also be pretty annoying but that seems like a card that won't see play unless sideboards exist. I do not think you need Disdain x3 right now but it's possible you will if the meta changes.
Pilgrimage is normally not necessary, but sometimes you will run into situations where it is handy - e.g. Smash 'Em All, being able to bounce a Greyseer or Ripped Bloodthirster.
I think City Gates is strong here - I've seen other listings running less than 3 and while I can see the argument for that I don't think it is correct. It essentially acts as extra drawing power once you have a Mine and it fuels your Strongholds and Innovations as well. And it's a building, so it triggers Treasure Vaults. It also gets around the 1 development per turn limit so your Strongholds can go crazy in a hurry. Do not forget it when calculating how many turns you have left before you deck yourself!
Wake the Mountain seems decent but you normally can't play it in the early game, so only 2x.
Temple of Vaul is good against slower decks - you can play it to Quest and that's your draw pretty much taken care of. I used to have more but in the current meta that doesn't seem good. In the midgame you don't really care about the damage if your Kingdom is still up as you can just pile more damage on the giant heap of developments.
Reap What's Sown is probably the hardest card in the deck to play. You will often just play it for as many as you can in the midgame but not always. Make sure you leave enough resources up for a Fog effect after you Reap.
Warpstones and Alliances usually go to Quest when you have a choice since they don't get boosted by Treasure Vaults.
On your critical turn against Dwarves, if you have the option, try to have 1 development already in your battlefield when you play the Thrower - otherwise they can demolish the Thrower in response to you developing. If you play the development first then they can demolish that to buy themselves a turn.
You may be wondering why there's a Judgement in here. It's because 1 Judgement in Order decks wins game 1 a surprising amount of the time against newer players. It's often dead weight but then you can just develop it. It has won me enough games to justify the slot.
The actual win condition is normally for you to get really far into your deck, then Gifts an attack, Flames at the start of your turn and hit them for lethal damage with the Thrower in a single turn. If you have time, it helps to have the Thrower out when you do that so you can get extra damage out of the Gifts resources as well as any you happen to have lying around.