How to run a Maven project from Eclipse?

Well, you need to incorporate exec-maven-plugin, this plug-in performs the same thing that you do on command prompt when you type in java -cp .;jarpaths TestMain. You can pass argument and define which phase (test, package, integration, verify, or deploy), you want this plug-in to call your main class.

You need to add this plug-in under <build> tag and specify parameters. For example

   <project>
    ...
    ...
    <build>
     <plugins>
      <plugin>
       <groupId>org.codehaus.mojo</groupId>
       <artifactId>exec-maven-plugin</artifactId>
       <version>1.1.1</version>
       <executions>
        <execution>
         <phase>test</phase>
         <goals>
          <goal>java</goal>
         </goals>
         <configuration>
          <mainClass>my.company.name.packageName.TestMain</mainClass>
          <arguments>
           <argument>myArg1</argument>
           <argument>myArg2</argument>
          </arguments>
         </configuration>
        </execution>
       </executions>
      </plugin>
     </plugins>
    </build>
    ...
    ...
   </project>

Now, if you right-click on on the project folder and do Run As > Maven Test, or Run As > Maven Package or Run As > Maven Install, the test phase will execute and so your Main class.

Your Maven project doesn't seem to be configured as a Eclipse Java project, that is the Java nature is missing (the little 'J' in the project icon).

To enable this, the <packaging> element in your pom.xml should be jar (or similar).

Then, right-click the project and select Maven > Update Project Configuration

For this to work, you need to have m2eclipse installed. But since you had the _ New ... > New Maven Project_ wizard, I assume you have m2eclipse installed.

(Alt + Shift + X) , then M to Run Maven Build. You will need to specify the Maven goals you want on Run -> Run Configurations