To upload your logo, login to your WordPress administration panel, and click into the theme options panel. The options panel will be noted in the WordPress sidebar and has the name of the theme. For instance in the screenshot below the options panel is labeled Simplicity Lite.
Once in the main options screen, click on the 'Settings' panel in the top tab bar:
In the first tab on the left labeled 'General', the first option is where you will upload your logo for display on your site, click the upload button next to the text field to open up the uploader:
Click the 'Select Files' button to upload the image from your computer:
Once you've selected the file on your computer and uploaded it, details for the image will display below the uploader, down at the bottom will be a button labeled 'Use this Image', click this button to insert the image into the text field. Once you've clicked this button the popup will close and your image will display in a preview box below the text field. Click the 'Save Options' button either to the right of the options screen or at the bottom of the page and you're all set!
Many themes offer the ability to adjust the spacing and positioning of your logo. These settings can be adjusted in the 'Styling' section of the options panel, under the 'Logo' tab on the left.