The main line from the basement is a clay pipe buried below ground. Its broken and sewage sometimes backs up. This line needs to be replaced. How can I replace this line with a newer pipe grade and what is the best way working with a situation like this.

Three ways I know of. 1) dig out and replace the line. 2) Use the trenchless pipe replacement method. Which is basically pulling a pipe through the same hole the old pipe leaves as it is crushed by the cone shaped head that is attached to the front of the replacement pipe that is hydraulically being pulled through the old pipe. Some digging is involved but complete excavation like the first method isn't necessary. 3) Relining the old pipe. This method involves adding a second skin to your present pipes interior. It is basically relining your pipe with an epoxy liner and essentially creating a pipe within a pipe.
There is another method I saw on TV that is similar to method 3 that uses a smaller diameter pipe that is installed into the old pipe and then inflated to create a new lining within the old pipe. It may actually be method 3 but is the only time I have seen it done.
If this repair doesn't involve going under driveways or under detached structures it may be most cost effective to dig it up and replace it. I'm sure you could get estimates and opinions from companies like roto rooter or local plumbers who are experienced and will be able to tell you which method would be the most effective and the costs associated with each.

I go with the Home_inspectiors option 1. The other options will likely not work since it sounds like there is already blockage or a collapse

Hi Ronnie...

Are you going to replace this or hire the work out? If you plan to do the work then let me know and I'll post information on materials needed, OK?

Mark