This--alerting me to environmental sounds to which I need to pay attention--is one of my girl Z's primary tasks. She tells me when several different timers go off, when someone is at the door, when the coffeepot is almost done brewing, when the cell phone rings or a text message is received, the smoke detector goes off, etc.
She initiated the smoke detector alert training. Shortly after I got hurt I was fixing dinner. I guess a fire started and the smoke detector went off; in the meantime, I had forgotten that I was cooking, and didn't notice the smoke detector. From my perspective, I suddenly had this absolutely insane 5 month old puppy bouncing off the walls and barking, racing from me to the kitchen and back. I went and checked, found and corrected the problem, and gave her a jackpot-sized treat.
Over the next few days, I'd use the "test" function to sound the timer, then give her treats. Now, anytime the alarm goes off, she finds me and makes sure I know it went off.
Other than that, training was basically as Lilie suggested.
For the coffeepot, I started by setting a bowl of treats on the counter where Z could see them. Then I sat in the next room and watching the pot brew. When it was making the gurgling noise that indicated it was almost done, I'd go to the pot; I suspect that from her perspective, she thought I was going to the bowl of treats, so of course she went with me! When we arrived, she was praised and got a treat. I shut the pot off and got a cup of coffee. Doing this every time, it wasn't long til she would tell me the pot was making noise.
Every time someone came to the door she got a treat. After a while, if I wasn't near the door, she would come tell me, doing the "running back and forth between me and the door" routine.
I began training her to alert to timers using the bell on the microwave, since I use it to nuke my coffee. I drink a lot of coffee, so there are lots of training opportunities. Same routine, it didn't take long for her to get the idea.
The cell phone was a different matter. I began training her using the alarm clock function, with the phone sitting by me. Then we worked on having it further and further away. During this process, she also had natural learning opportunities when someone would call (different ringtones) or text (a different sound--a 3 second tone), and when I had the ringer silenced so the phone just vibrated. She learned to alert me to the phone any time it made noise. (This has also made it my most-reliable alarm clock, because she will wake me to make sure I know the phone is making noise.)
She is the one who generalized the task (alerting me to alarms/signals/etc) to alerting me to the oven timer, washing machine timer, etc. A few weeks ago, she made sure I knew the tornado siren was going off; I've been meaning to train her for that but hadn't quite figured out how.