As with all "DIY"s, wait and see what everybody else has to say in response. This is how I did it. It is not "THE way", nor "the RIGHT way", just A way. For those familiar with OC jargon, "back chaining". Also compare with "targeting". If this way is incompatible with your choice of training methods, then don't use it - there are plenty of other ways.
The first step is to decide what you want as the behavior for "the basic alert". There will be other specialized alerts needed for special circumstances, such as fire or doorbell, but you need to decide what you want for the basic one, and you need to get it on cue.
I chose to have Mac signal me by placing his paw on my knee. He's too big for jumping on me, and since I keep his nails trimmed and don't wear stockings :-), it's a comfortable alert. You will need to make your own choices.
Put your dog into a sit in front of you, while you sit in a low chair. Gently lift his paw slightly and reward him. After doing that for a while, he should offer his paw. Give that a cue (command name). I gave that a cue of "SHAKE". Work with SHAKE until it is pretty reliable. Whoopee. You've taught him to shake hands. You might have a preferred way to do it.
Then, squeak a squeaker while giving the command "SHAKE". Very soon, you should get a paw offered by using EITHER the command "SHAKE", OR by squeaking the squeaker. A suitable dog will not have a problem with the idea of giving the same response to multiple different stimuli.
Once it is reliable, start to "raise the criteria". Only reward, or even acknowledge, the most enthusiastic responses. If you ignore his response, he will get insistent, and start to put his paw on your knee. THAT, you reward. Soon he will reliably put his paw on your knee whenever he hears the squeaker. The next step is to do it in other locations. Keep a squeaker in your pocket, one next to the toilet, one on the arm of your chair, etc. Do it everywhere. Do it with distractions. Once you can do it 5 times in 5 different places, with 3 different levels of distractions, do it some more!
As a further raising of the criteria, squeak the squeaker when he isn't right next to you. Get him to run to you to alert to the squeaker.
As an even harder further raising of the criteria, if there are helpers available, have somebody else squeak when he is next to you. When that is reliable, try having somebody else squeak when he isn't near you.
That is the basic alert. What's it for? Now you can begin training other sounds. Rig up a remote noisemaker, or set a timer of some sort to go off when you will be expecting it. When it does, squeak the squeaker. With enough repetitions, he will be alerting to that sound! Make a list of sounds for which you want the basic alert, and start in.
That technique is sometimes called "back chaining" - teaching the end of the chain of behaviors, and working backwards adding to it until you get to the beginning of the chain. The primary alternative method is to start with the sounds, reward any sort of response or even interest, and then work on shaping the response into what you want.
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(c) 1998, Fred and Mac