I would like to replace the default RTE in Sitecore with tinyMCE, how would I do it? Where do I start?
I went down this path in this question. To this point I don't think anyone has pulled it off. And its mainly because there is so much Sitecore functionality in the RTE (i.e. Links, photos, etc...) Your best bet it to just allow the editors to have a custom HTML editor similar to what Michael West did. You can wire in your client side editor the same way Mike did.
See his module here http://marketplace.sitecore.net/en/Modules/Code_Editor.aspx
A great video on it here http://youtube.com/watch?v=JgOSdjgG_qs
I'm supporting a Sitecore 6.5 site where TinyMCE has been used to replace the default rich text editor.
This article covers the setup https://sitecore.wordpress.com/2009/02/20/sitecore-forum-module-using-tinymce-instead-of-freetextbox/