How can I add legs to this piece in order to lift it up?

There are a few considerations: How far do you want it above the floor? How much weight will it be holding? What style do you want (if that matters) for the piece?

Perhaps something like this (style but not necessarily these exact since they are for chairs and screw in) if you don't want it very high off the ground:

https://www.amazon.com/Furniture-Tapered-Replacement-Suitable-Armchairs/dp/B07VDRY26D/ref=asc_df_B07VDRY26D/?tag=hyprod-20&linkCode=df0&hvadid=380037027829&hvpos=1o4&hvnetw=g&hvrand=13038114247504970940&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9011953&hvtargid=pla-818723231417&psc=1&tag=&ref=&adgrpid=79075834498&hvpone=&hvptwo=&hvadid=380037027829&hvpos=1o4&hvnetw=g&hvrand=13038114247504970940&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9011953&hvtargid=pla-818723231417

How about bun feet? There are so many styles to choose from.

It would depend on the weight of the articles in the bookcase, the desired height off the floor, or something to complement your decor. I was thinking of rollers so you'd be able to clean under it easily, they have a good selection at diy stores, Amazon, and a place called Harbor Freight, if you have one of them near you.

Hi! Something wide, rather than tall - you don't want it to get tippy. My new weird thing is to make sure I can fit my vacuum head under the feet of my furniture - it gets so gross under there if you can get the vacuum under! :)

I would so with some simple ones to compliment the trim at the top.

I go with Naomie. Bun feet. It wasn't really made for feet making it unstable.

They sell little bun feet at Lowe's I'd do that

Get some wide molding from Lowes or home depot. You can do this two ways. One is with mitre corners. the other is will the corner medallions. Then there is no miter cuts necessary. Use Construction glue to glue the frames. Oh when you paint, I used Rustoleum on one bathroom frame and latex paint on the other. The Rustoleum really protects against water stains. Latex not so much, and I did seal it. Remember to paint the back side at least 1/3 down because it can be seen on the mirror.

Bun feet would be perfect!

You cabinet will hold a lot of weight. You need sturdy legs which can be purchased at the hardware store or you can make wooden blocks, stain and place in all four corners of the cabinet by screwing into the bottom.

Examples of many different types of furniture feet available on eBay.