Democracy is a form of governance that is based on the concept that leaders can only lead upon the consent and the vote of the people that are governed.
Federalism is a state structure based around a central government which is formed after sovereign bodies agree to give up a portion of their sovereignty to form a single political unit.
The United States of America is an example of a democracy that is a federal state. While the central government has certain powers, this is only through the consent of the member states, and additionally the states have powers that the federal state cannot interfere with. Some forms of taxation and policing, for example, is in the purview of the states, since they have a level of sovereignty remaining from before they became a member of the US federation.
The UK is an example of a democracy that is not a federal state, since the members of the UK (England, Ireland, Scotland and Wales) are not sovereign bodies but parts of a single political body that is directly controlled by the central government (this is becoming a little more blurry with the rise of the Irish government, however the point remains the same).