The foreclosure process is started when the lender decides to file a Notice of Default against the borrower for missed mortgage payments. Some states only require the notice be filed at the local County Recorder's Office, while others specify that it must be an actual lawsuit handled through the courts. Regardless, the subsequent events will unfold in a similar manner. As soon as the Notice of Default is filed and the homeowner properly notified, consider that the foreclosure has officially begun.
It is difficult to pinpoint exactly when a Notice of Default will be filed. It varies from lender to lender; different companies have different internal guidelines. If you miss a payment, though, they will notice. Miss two or three and it is almost certain that the notice will soon be filed. Since regulations require that you be notified in writing and by a sign posted on the lawn of the property, there is little chance that you won't be aware of the proceeding.
Missing or even simply being late on even a single mortgage payment will do great damage to your credit report. It is to your advantage to do whatever you can to avoid that. A Notice of Default, however, does not necessarily mean the foreclosure auction is a done deal. The lender would prefer that you make up all delinquent payments and late fees rather than go through with the foreclosure. Foreclosures cost money for them. If you convince them you will be a good risk going forward, they'll rescind the Notice of Default.
The worst thing you can do, if you have hopes of staying in the house, is ignore a Notice of Default. Dodging the lender's phone calls and ignoring their letters is a swell way to create bad will and distrust toward you. Communicate with them and you might find an option to foreclosure. Loan modification or adding the past due amount to the end of the loan and increasing your payments to make up the deficit are a couple of suggestions you might broach. There's no guarantee they'll agree, but the odds are much higher if you're not a stranger to them.