This may not be exactly what you want but most people should know that you can create a 'movie' through a replay that you saved and upload it to the Forza Website. From there you can go to your gallery and find the 'movies' menu in your gallery. From here you can download the 'movie' you recorded and from there you can do what you wish and post it up onto YouTube. This though is a very long process, especially when you wish to combine multiple clips. From what I remember you can create a small amount of minor effects to spice up your video. If you wish to use proper equipment like an Elgato Gaming HD game recorder that plugs between the xbox and the device that it is meant to be recorded on, then you will have to buy one yourself or become really good friends with someone who has got one or something similar. No one would wish to spend their time recording for someone else when it won't benefit for them.
Good luck.
I don't always lead, but when I do...
I make sure I screw up the person behind me.