Hiya. My DS is almost 1 and those first few days at home seem like such a long time ago now!
You should have a midwife visit the day after you leave hospital. She will check the baby and you, and if you're bf will check that it's going okay which is your opportunity to get help if you're struggling. Other than that your first couple of days will be feeding your baby, trying to get him or her to sleep and then sleeping yourself if and when you get a chance.
Assuming you have a DP, his/her responsibility will be to look after you in those first days and to look after the baby to give you a bit of respite.
If you are bf, my main piece of advice would be to look after yourself first. If your baby is crying for food but you need a wee, then have that wee as you could be sitting feeding for the next hour or so. If you need a cup of tea, make yourself a cup of tea and THEN feed your baby.
The other thing I found helpful was to get up every day, have a shower and get dressed. Even though I wasn't leaving the house I found sticking to some kind of routine made me feel a bit more human rather than just staying in my PJs all day.
Also, don't worry if your baby fed/slept in hospital but doesn't feed/sleep easily at home. It will take your LO a while to adjust to being in a new environment and to be honest my DS never really took to his Moses basket in the way that I had hoped.
Finally, make sure that if you have friends/family visiting that you limit the time they are there so you have time to adjust being a new Mum. And when they are there, make sure they look after you rather than the other way round - having someone make you a cup of tea and a sandwich is a godsend in those early days.
Hope this helps!