Administrators protect pages and images to prevent vandalism and assist in resolving content disputes, for example. The key principle to remember here is that Wikipedia is the encyclopedia that "anyone can edit". Protecting pages defeats that goal and so page protection should be avoided when possible and kept as short as possible.
In general, the length of time used to protect a page is based on how long you think it will take for the contributor(s) to cool down and resume proper contributions. A 24 hour page protection is typical. If problems resume, the protection might be increased to 36 hours for example. The page protection history might help you figure out how long to protect the page by what has worked in the past for that page.
Protecting etiquette is very lax. Generally, you do not need to consult with the original page protecting admin and there usually is no reason to notify them after you modify a page protection. A log of protections and unprotections is available at Special:Log/protect.
Below are more detailed instructions for protecting and unprotecting pages. For this guide we will use the protection form provided by the MediaWiki software. However in practice you may more often use semi-automated tools to protect pages – namely Twinkle – which can make the process considerably easier.