Encountering foundables is one of the core gameplay aspects of Wizards Unite. Progressing through the game requires frequent encounter and they are an effective method of levelling up quickly.
One of the keys to finding the foundable encounters you want is to locate cluster spawns. Spawns are determined by data that contains areas of frequent cell phone usage. You can check where clumps of XM are in Ingress to determine where you can find cluster spawns in Wizards Unite.
Spawns will appear on the map as emblem looking symbols, known as traces. Each trace corresponds to a family from the registry pages through model and color. If you are looking to target a certain family of foundable spawns, find areas with the corresponding flag on the map.
During encounters, you will immediately be shown the difficulty of the encounter. Rare encounters will have higher difficulty, so be prepared with potions and your best spell-casting.
Spell-casting in Wizards Unite is one of the ways skill is incorporated into the game. Better spell-casting will result in more foundable encounters won. Speed and accuracy are both accounted for in spell-casting, however, speed is the prominent factor in masterful spell-casting.
Casting a spell requires Spell Energy. Spell Energy can diminish quickly, so make sure you are casting solid spells and frequently visiting inns to maximize the encounters you can enter.
Sadly, you are never given the choice to choose which spell to cast in encounters. Niantic has good reasoning for this though. The certain spells that are used make sense as to how the confoundable is defeated.
For example, Riddikulus is a spell used only for 4 foundable encounters: Harry Potter, Ron Weasley, Hermione Granger, and Neville Longbottom. Riddikulus is a spell that deals with boggarts, and all four of those characters are facing boggarts in those encounters.
Another example is Alohomora, the unlocking charm, freeing a Demiguise from shackles.
As you level up, capturing foundables will become much easier. Emergency threat level foundables are nearly impossible to overcome at low levels. They are also extremely rare, so use potions to make the most of them.
So far in the beta, traces seem to mostly lead to common foundable encounters. This seems much like the Pidgey and Weedle days of Pokémon Go. Hopefully Niantic makes rare spawns more common down the road, but for now, get out there and grind those levels.