You really did not mention your issue here. Were you able to access activiti-explorer ? If not check the configurations. A log file could help the people to understand the issue. You can also design and develop the BPM's in eclipse using activiti plug-in. This is one option which you could try. I really could not answer more than this here as your question was abstract.
My issue is, i have used alfresco-activiti 30 days trail pack. Deployed activiti-app.war file in Tomcat few months back. But now processes which i have created are not working.
Could you please tell me where to see activiti-app logs in tomcat.
I am not really sure how you can get your expired ones working so I just leave it to the forum to answer. Incase if you are starting new, you can always download a copy of activiti from http://activiti.org/download.html which is free and doesn't expire. You can also download an Activiti plugin into eclipse and build your processes there.
In the package you download, you get your activiti-explorer.war which needs to be deployed into the tomcat. The processes that you design using eclipse can be easily deployed into activiti with the help of activiti-explorer.
You can find the activiti logs in tomcat logs itself.