The BB on my bike has finally given up after a year or so of abuse.

Is replacement straightforward enough?
Is it just a case of knocking the old one out and pressing a new one in?
Can I do it without a proper press tool or not?

Dead easy, just like a headset. I use a mallet + screwdriver to remove, threaded bar + washers to install.

Yeah, just use a mallet ( plastic or rubber if possible ).

If you can, buy a metal PF BB, because the plastic ones are crap.