I work in a museum which has an extensive and extremely valuable library.
Do not use any type of adhesive tape or glues on your books. Over time, the glue can deteriorate, eating into the paper, staining it, or even causing the paper to “shatter.”
If you want to put covers on them, make sure they’re of acid-free paper, or archival-quality plastic. Some plastics “off-gas” which can stain and damage paper.
The most important thing to remember is anything you do to the book should be reversable. It’s best not to attempt any repairs yourself-- if the book is valuable, invest in having a professional do the repairs.
Do not use metal paperclips as marking devices, because these often rust. If you must write in the book, use a dull pencil. Do not leave bookmarks in the books to prevent staining.
Clean your books using a soft, dry paintbrush to remove surface dust. Dirt smudges on pages and mold residue can sometimes be removed with a talc-eraser. (It’s a powder in a bag which you gently rub across the page.) Here is the kind of eraser I’m talking about.
I would strongly recommend against doing anything other than a light, gentle removal of surface dirt. Doing it improperly could damage the book. At my museum, we always urge people not to try to clean anything up before they donate it to us-- even people who think they know what they’re doing can make horrible mistakes.
The best humidity level is between 40% and 50%-- but the main thing is consistency. Rapid humidity changes can cause the paper and binding material to swell. Ideal temperature is between 60 degrees and seventy-- the cooler the better, really. (We keep our most priceless books and manuscripts in a refrigerated vault.)
Storing books on shelves standing up is fine for books which seem sturdy. Group books of the same size together to keep them from being bent out of shape. Don’t shelve them tightly together, or push them all the way against the shelf-- air needs to circulate back there.
For books which are very fragile or have severe deteriotation, it’s best to store them lying flat. If the deterioration is partiularly bad, you may want to wrap it in a clean cotton sheet to protect it.
Keep them out of the light as much as possible, of course.
Some books are going to deteriorate no matter what you do because of something we in the museum field charmingly refer to as “inherant vice”-- meaning that the materials themselves are unstable. Chemicals in the paper (acids) ink, leather, and even the thread used for sewing the binding can be self-destructive.
It’s always best if you do not handle old or valuable books with your bare hands. Wear gloves to avoid getting skin oils on the paper.