I am replacing an existing old door with a new door. I am not replacing the frame only the door. How is the best way to ensure the new door into the same old frame.

Measure the old door then buy a new one that is the same size if possible. Is this an exterior door or an interior door?

It is a interior door. How much space is available for trimming the bottom and hinge side of the door.

That would depend on the door you choose. Some are hollow and have a limited amount of solid wood that can be cut off the edges, a solid wood door can be cut more. Try to get as close as possible to the existing size and cutting an inch or so off should not be a problem if it is necessary. What size is the door you would like to replace?

I placed the old door on top of the new door and aligned it up with the door knob hole. It appears that the bottom of the new door is about 1/2 to 3/4 inch longer. The door is hollow so that is why I was wondering about how much room I had to work with at the bottom. The hinge side is approximately 1/8 to 1/4 bigger than the old door.

Once I make the cut do I than line up the old hinge placement on the old door with the new door

The edges of the door are solid wood and you can cut 3/4" off the bottom and 1/4" off the hinge side if necessary, the trick will be getting the edge of the door routered for the hinges, look at where they go and see how it is recessed. The new doors hinges should line up with the old door. You might see if it will work without cutting the hinge edge first.

Thank you for your help with this. I was just making sure I was on the right track with the installation and hopefully not forgetting an important step.