One of the advantages of becoming a US citizen is gaining the ability to petition for relatives, like your parents. Often, this first comes us when parents are visiting their adult children and grandchildren in the US. Wouldn't it be great to be able to stay much longer and see the grandkids growing up? Traveling back and forth on a visitor visa works for many, but for others, it becomes cumbersome and for others, it may be next to impossible to obtain the B2 visitor visa.
Once you've made the decision to file, what's the right time to do so? As immediate relatives, the parents of a US citizen could be eligible to adjust their status in the US if they are otherwise legally present. This doesn't mean that parents may enter on a tourist visa with the intention of applying for a green card once they are here. In fact, that is potential misrepresentation and can lead to many future immigration problems. If your parents are here, however, having entered as visitors, and have a legitimate reason for changing their plans, filing for them in the US may be an option in the right circumstances. One caveat to filing an adjustment of status when parents are in the US, is that they will not be allowed to travel abroad during the processing until they are issued a travel permit (Advance Parole). To travel while an adjustment of status is pending without advance parole will most likely lead to the application being considered abandoned by USCIS.
For parents who are abroad, or who are visiting and will soon return abroad, the process for petitioning for them is known as consular processing (as opposed to the adjustment of status process mentioned above). The process is similar - you must prove you are a US citizen and that the people you are petitioning for are your parents. You will need to provide financial documents, and your parents will need to provide a police certificate as well as a medical exam in the later stages of the process. Birth certificates for your parents may pose a challenge depending on what country issued the certificates and if they were issued concurrently with the birth. The final interview takes place at the US Embassy in your parents' home country, and when they enter the US, they become permanent residents.
What about the travel issue for parents who are consular processing? The good news is that if they have a visitor visa, then usually they will still be able to travel to visit during most of the processing time. They should be prepared to show ties to their home country when entering the US, they should always leave at the appropriate time as governed by their I-94 and they should lessen the travel the closer they get to the Embassy interview.