Tourists from North America, Australia, Japan and the European Union (and many others, see link below) receive a visa upon arrival for up to 90 days.

When entering the country, you need to pass the immigration office (imigracion). There you get a stamp in your passport that states the number of days you are allowed to stay (usually 90 days). You can get an extension at immigration offices in any major city for 20US$ per month plus 26 soles administration fee. Make sure to take your time, don't expect things to be ready within less than an hour or even a day. The maximum extension allows you to stay for up to 180 days in total. When those 180 days are up and you would like to stay for longer, it's possible to cross the border to a neighbouring country (Ecuador, Colombia, Brazil, Bolivia or Chile) and return the next day and obtain another 180 days. Of course you can also leave the country before your first 90 days are over.

Furthermore, you will receive an extra official paper to be kept in the passport (make sure you don't lose it!). When leaving, you need to visit the emigration office (migracion), where you get the exit stamp. Imigracion and migracion are found on all border crossing-points. Extensions of the time to stay are no problem. Traveling to and from neighboring countries by land is no problem.