Download the Module
Go to http://drupal.org/project/modules and find the module that you want. In this example, we are going to install the Event module which is found in the Event category.
Once we click on search, we will scroll down and click on the module title, which in our example is event module.
Then download the recommended version.
Extract the Folder
To make the module easier to download, it is compressed (zipped) into one file using two levels of compression so we will have to extract it twice. Since it is a .tar.gz file, you may have to use a tool such as 7-zip (www.7-zip.org/) to extract the file, depending on your operating systems and the current programs which you have installed. Click on the file that you downloaded, then extract its contents. Next, click on the extracted file and extract its contents.
The end result of extraction is the module folder, which in this example is the event folder which contains the event module files.
Transfering the Module Folder to the Server
Now that we have our module folder, we need to move it to our server (using a FTP client or your host's file manager) to the appropriate directory. The best place to install the module is in the sites/all folder. The README.txt file explains that we need to create a new folder, "modules", that will store all our module folders, and also gives the explanation of why we install the modules here rather than in the /modules folder of our installation root (*this modules folder is not the same as the folder we will be creating; please read the README.txt).
Now that we have our modules folder created in sites/all, we can transfer the folder that contains the module files that we want to install (in our example the event folder) .
Make sure you are in the modules folder that you created, then upload the module folder that contains the module files that you are installing (in our case, the event folder) .
Enable the Module via Administer
Now go to your site and log in as an administrator and then go to Administer.
Click on Site building, then Modules.
Scroll down to find the module that you installed. Once there, simply select which features you want enabled, then save the configuration. Do notice requirements of the module (within the description) as those must be met in order to enable the module.
That is all! You have just installed the module and enabled it and you are now ready to use it.