Create your own logo and upload it to the /templates/your_template/images folder. Lets say,you want it to be 450x95 pixels in size. Depending on the background of your site, consider making the logo with transparent background, and saving it in a file format (say, png) that supports it.

In administration, go to Extensions > Template Manager

Click on your_template, you will access the Template edit page

Click on Edit CSS

Select template.css and click edit

The easiest way is pressing CTRL + F . Its the command for FIND. Just find the term LOGO and you will see the LOGO CSS definitions.

Another way is to look for the div#logo style. It should look something like this:

div#logo {
        position: absolute;
        left: 0;
        top: 0;
        float: left;
        width: 298px;
        height: 75px;
        background: url(../images/mv_joomla_logo.png) 0 0 no-repeat;
        margin-left: 30px;
        margin-top: 25px;
}

The line you are interested is the one beginning with background. Change the path of the image to the image you have uploaded. If you put your image in the your_template/images folder, all you would have to do is replace mv_joomla_logo.png with you logo filename.

Click on Save.

Thats it!!