Advice on working out after beign sore from the day before

I think there are different levels of sore. If you're feeling a bit sore and achy, make sure you are stretching and warming up/cooling down. I find on days I skip the warm up, my muscles get more sore.

If you strain your muscles so hard you can barely walk or lift your arms, take a day or two off. First day I started resistance and weight training I did one-legged glute bridges as described in the plan I was following. The next day those muscles were so sore and tight I seriously could barely walk and was limping all over the place. That's when you might want to take a day or two off, lol.

Also might want to invest in a foam roller and massage any persistently sore muscles to release the tension, they're cheap and totally worth it.

if your muscles hurt because you haven't trained it in that way much or before, then the soreness is awesome because it means you are building the muscle. If you want to work on the same muscles again, you probably need at least a day break for the muscle to repair itself and learn how to protect you from the same exercise next time. But you don't need to wait for the soreness to go away, in fact most of the time that type of soreness feels better when you exercise or walk. It can be worse on the second day though (pain wise), so you can take a pain killer and still do your workout.

Slow achey pain that shows up the day after is good, sharp stabby immediate pain while exercising is usually bad.

It is better to work through the soreness than to let your sore muscles sit until they are not sore anymore. I have noticed that if you work through it, they "heal" faster and you won't be sore for as many days as you could be if you didn't work out at all days after. My advice would be to stretch the sore muscles (lightly and not painful) but do most of your work out for parts of the body that are not sore. I meet with a personal trainer twice a week and we stretch and do light exercises to help the sore parts of the body and then focus more on other parts of the body that are not sore.

I do agree with taking rest days if you have injured yourself. Most of the time, you will be able to tell if you are just sore or if something is really injured. Myself and a lot of people I have been around are encouraged to take rest days even if you feel you do not need them. Letting your muscles heal is as important as building those muscles.

Switching up your routine by changing what muscles and exercises you will do that session will keep you motivated and less likely to be sore every time. Proper technique and warm up/cool downs will help with soreness as well.