How to straighten out tapestry?

Iron and starch it? I use my flat iron (for my hair) to straighten out collars and ribbons. Maybe that will work also for the ends?:-)

If it doesn't need dry cleaning, iron it out on a low setting. You didn't mention what type of fabric, so I'm offering the least damaging advice.

Stretch and steam with clothes steamer. Iron might cause damage

A dowel on the bottom might help.

If it's not valuable you can make a flat lightweight 3-sided frame and attach it to the back. Use a fabric glue on the wood and adhere it to the back of the tapestry. Weight it down and let dry thoroughly. Rehang.

Is the tapestry hand made or machine made? I think you need a lining for the tapestry or at least an inside binding for the edges of the tapestry.

I've had this problem and solved it by hand sewing ribbon loops at the bottom of the tapestry back side (if scalloped botton, sew loops above the highest part of the scallop edge). I spaced the loops every 12 inches with the exception of each end being placed two inches away from the actual end. I then inserted a 1 inch dowel through each loop. The dowel kept the tapestry straight and prevented the edges from turning in. My tapestry was lined so I matched the ribbon loops to the lining color and painted the dowel to match. Was very easy to do.

Small World!