Becoming a U.S. citizen through Naturalization?

One of the ways of becoming an American citizen is through a Naturalization Process based on 3 or 5 year rules.

If you marry a US citizen, you may apply  for citizenship under the three years rule if all other eligibility requirements are met. If not, you will have to wait from the date you become a green card holder 5 more years. During these 3 and 5 year rules, you will have to maintain "continuous physical presence" in the United States to be qualified to apply for citizenship if other eligibility requirements are met.

What is considered a "continuous physical presence" in the United States ?

Generally, "Continuous Physical Presence" means that you may not leave the US for more than six months, to be safe I would recommend to stay oversea about five months before returning to the US. This means if you stay outside the United States for more than six months you may break the "continuous presence" rule and you may not qualify to apply for US citizenship even if all other eligibility requirements are met.  Once you break the rule, you will have to restart the calculation under the "4 year and 1 day rule." Although 6 months but less than 1 year does not automatically break continuity, but it is presumed to break continuity unless you prove USCIS otherwise. You could show you kept your job in the U.S. while oversea, strong family ties in the U.S., properties in the U.S., etc But it is better you make sure yourself than regretting later if you really want to be a U.S. citizen.

It requires you to have been physically present in the U.S. for at least 30 months out of the total 5 year period  or 18 months of the 3 years period if the reduced period applies before filing for N-400.

What is the "4 year 1 day rule" for U.S. Citizenship?

The 4 year and 1 day rule mostly works as follows. 

Once you've broken continuous residency, a new period will begin to run on the first day you return to the U.S. From that day you must stay in the U.S. for a minimum of 4 years and 1 day before you can apply for naturalization again. This rule applies to permanent lawful residents (i.e. green card holders) who were required to be in the U.S. for a continuous period of 5 years but who broke the continuity of their residence. For those who are married to US citizen and still living together, the period of calculation is  usually 2 years and 1 day rule before applying for U.S. Citizenship if "continuous physical presence" has been broken.  I would recommend waiting at least 4 years and 6 months for 5 years of "continuous physical presence" requirement and 2 years and 6 months for those married to U.S. citizens if all other eligibility requirements are met.

Maintaining continuous residence requires you to maintain a permanent dwelling or principal residence in the U.S. You may travel oversea as long as you do not have a single absence which is long enough to "break" continuity for naturalization process.