The support section of the MultiBit website shows a completely different UI as well as many options that the current version doesn't have.
How can I find my private key?
If you want to use the original version of MultiBit (called MultiBit Classic) then the installers are available on the https://multibit.org website.
Click on the 'Download' button at the top of the page and then look at the bottom of the 'Releases and signatures' section.
The new version of MultiBit (called MultiBit HD) uses a set of wallet words to deterministically generate private keys and addresses. You restore directly from the wallet words rather than exporting/ importing individual private keys.