Documentation of Composer can be found at getcomposer.org/doc, especially Troubleshooting section. Usually the dependency problems comes from misconfiguration of your composer.json and understanding Composer logs comes with experience or learning on trial and error. Documenting every possible errors out of hundreds can become quickly outdated. If you believe some specific error isn't clear enough, you can always raise a new suggestion at the Composer's GitHub page.
As suggested in linked GitHub issue, "Conclusion: don't install" message it could be related to requirements defined in minimum-stability. Another linked question could be related to Composer's bug as reported at GH-7215.
Errors
Here is a small guide explaining the common Composer's errors:
- 
Can only install one of: org/package[x.y.z, X.Y.Z]. 
 If you see this messages, that could be the main cause of the dependency issue. It basically means that based on the Composer's dependency calculation both of these versions are required, but only one major version can be installed (you cannot have both x.y.z and X.Y.Z, unless you split your configuration for different folders). To see whythese packages are required, use thecomposer why/dependscommand and adjust the dependencies accordingly.
 See: How to resolve a "Can only install one of:" conflict? & How to solve two packages requirements conflicts when running composer install? 
- 
Installation request for org/package2 (locked at vX.Y.Z) 
 This message means that there was an installation request for org/package, however, it is locked at X.Y.Z. If the requested version is not compatible with the locked version (like a different major version), you cannot install both. This message often comes along with already mentioned "Can only install one" one. So, whenever you see "locked at", that means Composer reads your installed package version from the composer.lockfile. To troubleshoot, you can usecomposer why/dependscommand to find why the package was requested and adjust the compatibility, otherwise, you may try to removecomposer.lockfile and start from scratch (ideally from the empty folder).
 See: Installation failed for laravel/lumen-installer: guzzlehttp/guzzle locked at 6.3.0 
- 
org/package1 vx.y.z conflicts with org/package2[vX.Y.Z]. 
 It is a similar issue as above where two packages are conflicting and you need to solve the dependency manually. Reading the whole context of the message may give you some more clues. Checking the dependency tree may also help (composer show -t).
 
- 
conflict with your requirements or minimum-stability
 
 This message means as it reads, so you should check the required version and/or your minimum-stabilitysettings.
 
This can be caused by a package being marked as non-stable and your requirements being "stable only. See: But these conflict with your requirements or minimum-stability
Or because of conflicts with other installed packages. See: How to identify what is preventing Composer from installing latest version of a package?.
For any other errors, check out the official Composer's Troubleshooting page.
Troubleshooting
Here are more suggestions how to troubleshoot the Composer dependency issues in general:
- Add -v/-vv/-vvvparameter to your command for more verbose output.
- Run composer diagnoseto check for common errors to help debugging problems.
- If you seeing "locked at x.y.z" messages, it relates to packages locked in your composer.lock.
- Test your composer.jsonon the empty folder.
- Keep your composer.jsonto minimum.
- Run composer show -tto see your current dependency tree.
- Run composer show -a org/package x.y.zto check the details about the package.
- Feel free to ask a new question at Stack Overflow.
To fully debug Composer's dependency problem, you can:
Useful threads explaining common errors: