This is a guide explaining how to get logs on various launchers. If there is a launcher you want to see added reply in the comments. You can also see this guide from CrashDetector which explains how to get launcher logs for more launchers with pictures.
Once you have logs you can either upload them as an attachment if they are in the form of a file, or if its in clipboard format you can put on a paste website.
This assumes you have file extensions turned on (.log .txt and others), it is recommeneded that you enable them. If not your files may not show them and will look a bit different (such as latest.log will appear as just latest).
Vanilla Launcher (Official one provided by Mojang)
Minecraft Server
MinecraftForge Installer
ModLists
Note: We are not officially affiliated with any of the 3rd party launchers, we cannot fix their errors and cannot attest for differences or problems in them and are going from personal experience.
CurseForge Launcher
TLauncher
MultiMC/Prism Launcher (and derivatives)
GDLauncher
ATLauncher