It should be pretty straightforward. When you buy a new doorknob, it will come with instructions. All you really need is a screwdriver.
Just ask your landlord first. I used to live in an apartment where we wanted to put a locking doorknob on the front door (it came with only a deadbolt). The landlord was fine with it as long as we left a key with them and re-installed the old knob when we moved out. Unfortunately, when we moved out, the movers packed the old doorknob, so the landlord replaced it with a non-locking knob and took the cost out of our security deposit.
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