Update July 2018: Uzbekistan has launched eVisa portal that allows Indians to apply for visa without depending on travel agents for a Letter of Invitation. Please refer the following links for eVisa application. I have not used it personally but feel free to share your experience in the comments section.
The below content is based on my experience from 2014 and I have retained it just for nostalgic reasons. Please refer the above links for updated information regarding Uzbekistan visa for Indians. Thanks Sarai for this update.