How do I connect regions city to city to expand im new to sim city 4
Have you done the in-game tutorials? Those should teach you about that. Also, read through the manual. If you bought SimCity on the internet, just Google search for "Simcity 4 manual" and you should find a PDF version. Once you do the tutorials and read the manual, you should know all of the game basics.
In case you don't find help from those, you connect with Roads (or highways, avenues, rail, etc.), Power Lines, or Water Pipes. Road connections connect traffic and help industrial demand, power and water allow you to share those commodities between your cities.