Day before yesterday our shower broke. I went in to use the bathroom a while after one of the kids took a shower and I noticed there was a drizzle coming out from behind the shower knob. Thinking that the water wasn't fully off, or the plunger on the spigot that turns the shower on/off wasn't fully engaged, I turned the water back on, turned the shower on, turned the water off. But the leaking was still going on. Told my hubby what was going on, and went downstairs to do laundry.
When I went down, there was a whole lot of dripping going on into the basement. I flaked and by the time I had set up a bucket, my hubby already had the knob/cap and sleeve off the faucet in the shower. That seemed to slow the drizzle to a steady drip out of the end of the pipe sticking out of the wall. We decided to stop there since neither of us are really plumbers.
The good news is that the drip into the basement completely stopped overnight. The bad news is we still need to fix our faucet, since it is now a pipe sticking out of the wall with a slow steady drip coming out of it.
It is a single knob handle, Moen brand. The on/off plunger for the shower is in the top of the spigot. The big plate around the pipe is still attached to the wall. Two screws below the pipe appear to hold the plate in place.
So I'm reading around. I think we might just need to replace the core bit of the pipe sticking out, but I'm not sure. I'm a little scared to go yanking on anything and making things worse. Do I just need to replace the core bit while the plate is in place, or do I need to take the plate off to see if something else is causing this problem?
Is this a DIY or call a plumber?

Moen single handle tub/shower cartirdges are (usually) easy to replace. Shut water off to house, then remove the cartidge and put in a new one. This should take care of all your leakage problems. You should be able to leave the faceplate on when changing out the cartride. There will be an upside down horseshoe shaped retaining clip that will have to be removed before you can pull the cartridge. (make sure to put it back in before turning water on). There are a few folks here that have links to videos that show how to replace cartridge, and also will give you the number to moen so you can call them and get the replacement part for free(yep, moen, lifetime warranty). Just let them know what style of fuacet you have. Does the handle pull out, then turn left or right for hot and cold, or does the handle point straight down and as you turn it counter clockwise, it goes from from cold to hot. Should be an easy diy job either way. Good luck and please do let me know how things turn out.

Thank you so much, you gave me the answer I was hoping to hear. Pull out L/R style, think I can tackle this :)