Assuming you are talking about Dynatrace AppMon (and not Dynatrace Saas/Managed):
First I would see if something is being written to the agent log file (located in the install directory\logs). If something is being written there then it means that at least the application process has loaded the agent. In there you might be able to find some clues such as unable to connect to collector. If it is unable to connect, make sure that all required firewall ports have been opened and the collector is running and connected to the AppMon server.
If nothing is being written to the agent log, make sure that the application/web server has been correctly configured to load the agent. Which type of agent are you referring to? Some links to the doc which can help you out: java.net. The application logs can point you to the issue:
maybe a spelling mistake in the -agentpath parameter.
Maybe the user that starts the application process has no access rights to the agent installation folder
make sure you load the correct architecture agent (32 vs 64 bit)
These are some quick checks you can perform already.