If lined, really should have dry cleaned.
Molly, be aware that the drapes will most likely shrink some if they have never been cleaned before. When I had an interior design business, the information given to me by the drapery factory to pass on to my customers was to spot clean them, vacuum regularly, and that's it. Most fabrics shrink at least a few percent, but that's at least a few inches -- and if you spent thousands on professional draperies (or even hundreds on ready-mades!) you don't want to have to move the rods down because they are now too short!
Every day cleaning I vacuum them. My living room drapes are silk and lined. They go to the dry cleaners twice a year. All other curtains get washed and ironed on an as needed basis.
It would highly depend on the construction and fabric material of said drapery. I have 100% silk dupioni drapery that is lined with a linen cotton blend – they go straight to the dry cleaners to preserve the color, finish and avoid shrink. I have poly sheers that I wash on gentle cool and they come out near dry so I just pop them in the dryer for 5 minutes to fluff and hang right back up. I have had to fix a hem here and there but they have lasted me 20+ years. I previously had some valances that were cotton poly blend that would have held up to machine wash if it were not for tassels attached, so those I just hand washed in the bathtub and drip dried on the clothes horse. My insulated “silk look” curtains from Target, machine wash gentle cool, 5 minute fluff in dryer and re-hung to dry in place. If you have fancy drapes – send them to the cleaner. If they are plain easily replaceable treat as gently as possible with at home cleaning. If you are a renter and the drapes were there, ask your landlord how they would clean them…If I had dry cleaner drapes in my rental, I would expect to pay for professional cleaning and not put that on my tenants. Be aware that professional cleaning is very expensive for drapery. My silk drapes are $80 a panel to clean but then again they are $300 a panel to purchase them. With proper regular shaking, vacuuming and lint rolling in my rather clean environment, I only send them out every 5 years or so. They are now almost 20 years old and in perfect shape like the day I purchased them.
Thank you for your advice. Molly