Download the latest version in the 'Downloads' section. After registering you will receive an email with the download link. If you do not receive an email, please check your 'Junk E-mail' folder. It might have been flagged as spam since it is an automatically generated email. Unzip the folder containing the MaxQuant binaries. Make sure that your computer fulfils the hardware requirements and that all necessary software components are installed. You start MaxQuant by double-clicking on MaxQuant.exe. A getting started document you can get in the main menu of MaxQuant under Help -> Getting started. In case of problems you may find answers to your questions in the frequently asked questions (FAQ) section or you may consult the MaxQuant Google group. Your question may have been posted already which you can find out with the search functionality. You can find further information about the meanings of columns in the output tables in the document 'tables.pdf' which will be written by MaxQuant into the folder 'combined\txt'.
Perseus is designed to perform all downstream bioinformatics and statistics on the MaxQuant output tables.
While it is most convenient to use the Andromeda search engine as part of MaxQuant you can also download the standalone version.