So I had just had a shower upstairs this past weekend and went downstairs to do the laundry and I discovered that the floor near the pipes was wet. See photo

I immediately went and bought some GOOP and sealed the cracked section of pipe and then I called a plumber to fix it and he said he would be able to handle it sometime this week. Well I never heard back from him (we've had crazy terrible weather) and now I'm thinking that maybe I could just do the work myself.
How do I replace a drain stack?