Traveling to Azerbaijan is very easy.
The international airport of Baku has many connections to Europe and many other countries in Asia and the Middle East.
Georgia – There are two very friendly open borders with Georgia, one linking Zaqatala with Sighnaghi and other one linking Ganja with Tbilisi. The second one can be crossed by train and, in fact, there is a direct night train from Tbilisi to Baku.
Iran – The border with Iran is also open and very friendly but remember that, if you are going to Iran, you will need to be in possession of an Iranian visa.
Russia – Also you can travel to Azerbaijan via Russia
Kazakhstan – You can travel to Azerbaijan by boat over the Caspian Sea from a Kazakh city named Aktau. It takes 24 hours and you need a dose of patience because it departs every few days, randomly.
Turkmenistan – If you are lucky to be in possession of a Turkmen visa, you can also take the boat from Turkmenistan to Azerbaijan.