The general upgrade guide should be followed
Note: there is one required update to the web.config, the ExamineLuceneIndexSets section has a changed type, the new type should be: Examine.LuceneEngine.Config.IndexSets, Examine
There are other minor changes in config files but they're not required nothing will break if you don't apply them.

Upgrading from older versions?

Whats new

1 ninor breaking change to drastically improve sorting - read about it in the related issue
Updates to caching and load-balancing
Improvements to hostname/language management
Improvments to sorting, publishing children and required field validation
UmbracoApiController for using ASP.NET WebAPI with an Umbraco context
MiniProfiler added (see blog post)
Public request pipeline
Relations API
PetaPoco now has a retry strategy to support SQL Azure better
Note: The umbraco.webservices dll is now a seperate download
A full list of changes for 6.1.0 is available from the issue tracker
Changes in 6.1.1

Note

The code editor has recently been greatly improved, but is sometimes problematic in Internet Explorer 9 and lower. Previously it was just disabled for IE and we recommend you disable it in umbracoSettings.config (scriptDisableEditor) if you have problems working with it.