Elections in the United States occur in two distinct phases: primary elections and general elections. During the first step, the Spring primary election, voters will choose which candidates are put forward for each political party. These primaries may be either open or closed, depending on each specific party's rules, which will determine if voters who are not registered with any party (NPP -- "No Party Preference") are able to request a ballot and participate. If you are registered NPP and want to request a specific party's primary ballot, you may contact the Secretary of State's office to check if that party has an open or closed primary.
In the Fall general election, you will notice that your ballot will begin with candidates for federal office; depending on the year, this may include Presidential candidates, as well as candidates for the Senate and the House of Representatives. Next will be candidates for statewide office, which may include candidates for Governor, State Senate, State Assembly, and Treasurer, among other offices. This will be followed by candidates for local office, such as your city's mayor, your county sheriff and district attorney, and local judges. (These statewide and local candidates will also be on the ballot in the earlier primary election.) Finally, the ballot will conclude with a series of Yes/No ballot measures, which will include both statewide propositions and ones being considered at your local city / county level.
This can all feel very overwhelming and confusing, especially when it may not be clear what a ballot measure is actually intended to do or what every candidate stands for. Elections for local offices in particular tend to be non-partisan races, meaning that you won't know a candidate's political party or ideology based solely on what the ballot says. However, websites such as Ballotpedia and Vote Smart (both featured in this page's "Online Resources" box to the left) can be useful places to do further research that will help explain what a ballot measure says or give you further details about who a candidate is.
For local candidates who are particularly difficult to identify, you may also wish to consider the following strategies: