This is a good example of a simple custom web part. It has the basic code to get your head wrapped around the process…
http://www.fivenumber.com/custom-webpart-inserts-items-into-sharepoint-custom-list/
This link gives you the how-to around deploying your custom web part…
http://msdn.microsoft.com/en-us/library/ms415817(v=office.14).aspx
