If installation of LanguageTool in LibreOffice/OpenOffice didn't throw an error but you are not sure if it actually works, please load this document and follow the instructions in it.
Common issues
LibreOffice comes with its own integrated grammar checker (LightProof) which disables LanguageTool for English and Russian. Use Options -> Language Settings -> Writing aids -> Edit... to disable LightProof and enable LanguageTool for the language you are working with to make LanguageTool work.
Make sure Java 8 or later is selected in LibreOffice (Tools -> Options -> Advanced) or OpenOffice.org (Tools -> Options -> Java). For Mac users: LibreOffice (Preferences -> LibreOffice -> Advanced).
Note that if you have a 32-bit version of LibreOffice/OpenOffice, you will also need a 32-bit version of Java - LanguageTool will not work otherwise. Apache OpenOffice doesn't provide official 64-bit versions for Windows and Mac yet, so you will need a 32-bit Java on Windows and Mac.
If you get "Could not create Java implementation loader": If you have this problem on 64-bit Windows, it may be caused by a 64-bit version of Java. Apache OpenOffice on Windows is only built as a 32-bit application and will not work with a 64-bit Java. You need to use a 32-bit build of Java for Windows. (OOo bug #118346). If that doesn't help, please try these suggestions.
Other issues
If you get "This media-type is not supported: application/vnd.sun.star.package-bundle2.0.00" during installation, please consider resetting your OpenOffice user profile.
If you get an error that says "Invalid memory access", make sure LanguageTool is installed in a path that has no special characters (use a-z, A-Z and 0-9 only).
If you get "Failed to load rules for language ... Caused by java.lang.ClassNotFoundException: Loading rules failed: Duplicate class definition": For some reason LanguageTool is installed twice as an extension in LibreOffice/OpenOffice.org. You can try deleting the directories listed in the error message after making a backup. (The directories to be deleted have random names like "EE31.tmp_" or similar - exit LibreOffice/OpenOffice.org before deleting anything).
If LanguageTool still doesn't work properly for you, please post to the forum describing the problem and letting us know which version of LanguageTool, LibreOffice/OpenOffice.org and which operating system you are using.