Phone or Tablet Data Loss
Data loss on a phone or tablet doesn't play by the same rules as a PC, mostly because of two things nearly every modern smartphone does that a typical computer doesn't: encrypting all storage by default, and soldering the flash memory directly onto the board.
What's actually happening
Because encryption is on by default on essentially all current iOS and most Android devices, storage that's physically extracted from a damaged device — because the screen is unresponsive, the device won't boot, or it's been through water — is unreadable without the device's own passcode-derived key, even if the physical flash chip itself is completely intact. This is the opposite of most scenarios in this catalog: the barrier is usually not damage to the data, it's access to a device that can decrypt it.
How recoverable this really is
Strongly depends on what the actual failure is. A cracked screen or a dead charging port, where the device otherwise still functions internally, is often the most recoverable version of this — connecting the device to a computer, or repairing just the broken component, can restore full normal access. A device that won't boot at all, or that's been physically destroyed, is a much harder problem specifically because of the encryption point above: data extraction at the chip level is possible in principle but generally requires the device's own passcode to make sense of what's extracted.
The general approach
Where the device still partly functions, recovery focuses on getting any form of data access working again — an alternative display path, a repaired port, a boot into a recovery mode — since that access, combined with the correct passcode, unlocks everything at once far more reliably than any deeper extraction attempt. Where the device doesn't function at all, options are genuinely more limited and device-specific, and usually depend more on whether recent backups exist — a manufacturer cloud backup, or a computer the device was previously synced to — than on any recovery technique applied to the device itself.
Don't try to guess past a screen lock or passcode by entering random combinations repeatedly. Most mobile devices impose an escalating lockout, and some, particularly iPhones, can wipe themselves entirely after a set number of failed attempts. If the passcode isn't known for certain, stop before guessing.
Practical, step-by-step guides for specific recovery software will be added here as separate linked articles.
This page describes the general situation, not a guaranteed fix for your specific case. If you'd rather have someone experienced take a look before you try anything, see what a hands-on evaluation looks like.