Step 1. Download Tomcat7 Binary Distributions from Tomcat homepage.
Step 2. Move the downloaded directory to /usr/local:

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sudo mv ~/Downloads/Apache-tomcat-7.0.24 /usr/local

Step 3. Create a symbolic link in /Library:

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sudo ln -s /usr/local/Apache-tomcat-7.0.24 /Library/Tomcat

Step 4. Change ownership of /Library/Tomcat:

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sudo chown -R <user_name> /Library/Tomcat

Step 5. Make all scripts executable:

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sudo chmod +x /Library/Tomcat/bin/*.sh

Step 6. Use command /Library/Tomcat/bin/startup.sh to start tomcat, then brower http://localhost:8080.