I am scheduled for Cataract surgery on my right eye. I will be having a toric IOL for distance. Since my left eye will be left alone for now, how would I see up close and at what distance would I need to wear glasses.

Need reading glasses. A toric IOL means it corrects pre-existing astigmatisms. It is not a bifocal lens. If it is calculated for distance you will need reading glasses & multifocal readers so you can see at most distances. Just like your left eye has probably a multifocal glass the right glass will have the same. Barring any complications or preexisting problems, then you should be able to read at almost all distances.
Vision post cataract. The iol should correct the distance vision in your right eye. You will need near correction. Don’t have info to discuss the left eye.
Depends . The cataract surgery performed to correct your astigmatism and refractive error will help to bring things in the distance in focus. If the target is hit, then this eye alone will need some help to see up close (readers or prescription). Your left eye however could already be nearsighted, which could help you see up close. If not, you will still need glasses of sorts. There are various solutions. .
Near glasses. I assume that your left eye sees well and the right eye is corrected for distance. After healing you can see at near with over the counter reading glasses of +2.50 to + 3.00 power. You would need these for near and nothing for distance with these criteria.