Changing cooling fluid it's a bit tricky process but it can be done by yourself. The whole process will take 1–2 hours because you need to cool down the engine, and it will save you up to $150.
To replace coolant in 1998 Audi A8 first you need to flush old fluid. Start with a cool engine. Drain the overflow reservoir first, then open the radiator cap, and open the radiator drain cock. After that check for cooling fluid drain plugs on the engine block. If your car have those unscrew them and drain coolant from the engine block. If you want to clean the system pour coolant cleaner and start the engine. Read the coolant cleaner manual and follow the product directions. Then flush coolant cleaner as you've flushed coolant before. The final step is to pour new coolant.
Please be noted that all capacities listed here are approximate. Check fluid levels when adding or refilling as recommended in your 1998 Audi A8 user's manual. Keep in mind that all information here is provided “as is” without any warranty of any kind.
Before doing any DIY service please check your insurance policy and Audi warranty policy for your region. In some regions DIY service may invalidate your warranty.
DIY car service is not as difficult as it looks like and it might save you thousands of dollars per year. It might be even fun and a good thing to do with your kids on a weekend to teach them how basic machinery works. It's really hard to screw something up and damage your car permanently if you use right tools, follow Audi A8 service manual and use right parts and fluids in prescribed amounts. Even modern cars stuffed with electronics can be serviced in your garage or even in your driveway. Changing engine oil, brake fluid, ATF, replacing brake pads, and etc. It's all may be done by yourself in a mater of a couple of hours.
Doing basic service for your 1998 Audi A8 you're not only saving money, but also also improving your technical skills and learning something new.