For general materials, like iron and diamond, digging while being patient is your best bet. Alternatively, cave exploring might be more your thing. Note that certain materials only spawn below certain Z levels, so if you’re not finding what you need, you may need to go deeper. Diamond and redstone, for example, are easiest to find on the same level as lava.

Once you have a diamond pickaxe you can mine obsidian (pour a bucket of water on lava) which is needed to build a nether portal.

Materials:

Coal and emeralds are usually higher up in caves, where stone is (emeralds much less apparent, best obtained through trading with villagers), and are rarer the further down you go. Iron, copper, and lapis lazuli are found almost throughout all height levels of cave. Gold, diamond, and redstone usually start around where stone-meets-deepslate, and further down. Ancient Debris is only in the Nether, and far down in the layers of netherrack.

Some non-ore materials, like bamboo, dripstone, moss, amethyst, coral, prismarine, etc., just require exploring the right biome to find them.

“Templates” are usually in chests of points-of-interests (below).

Points of Interest:

Really the best way to find most of these are just exploring. If your world is oceanic, consider a boat or boat-with-chest. If the world is continental, maybe consider a horse/donkey/mule/camel (if you stumble across a saddle).

Some PoI’s are common-ish enough where you’ll probably find at least one just by exploring, or exporing the right biome. Shipwrecks and underwater ruins in the oceans, pyramids in the desert, villages and incomplete nether portals in most biomes. These you just have to stumble across them, and you’ll know when you see them.

Some PoI’s are very hidden, and really require luck and time to find, like “old-style” dungeon spawners, Ancient Cities, Trail Ruins. Trail Ruins in particular, you can spot them from the surface if you notice the terracotta and/or suspicious gravel (which looks like gravel at a glance, but it may be out-of-place next to dirt/grass), but they’re pretty rare to find. Ancient Cities are always in the Deep Dark, but requires a lot of digging/wandering around blindly to find due to the rarity. The old dungeon spawners are very obvious if you stumble across them, it just looks like a cobblestone cube with mossy-cobblestone mixed into the floor, and the spawner cage in the middle. Nether fortresses look like bridges and buildings of dark-red netherbricks. Piglin Bastions are giant towers of blackstone (plain, bricks, etc), with some guilded blackstone scattered in.

Strongholds, can be found with Eyes of Ender (obtained later in the game, after killing Blazes and Enderman for their Blaze Rods and Ender Pearls respectively).

Some, like Woodland Mansions, Ocean Monuments, and Trial Chambers (in 1.21) can be found by leveling up a Cartographer villager and purchasing the corresponding map from them.