One mandalam is 41 days. The vritham you follow during that period is called Mandala Vritham. The period begins on the first day of Karthikai month (Hindu calendar) around middle of November (Nov 15th this year) and ends around Christmas (Dec 24th this year). After observing the vritham for 41 days, the Ayyappa devotee prepares irumudi and proceeds on the holy trek to see Lord Ayyappa at Sabarimala. Now there are 2 routes to go to Sabarimala - the recent short route from Pamba (11+ kms trek) and the traditional long route from Erumeli (about 60kms). Even today, when you take the long route it takes 2 days to reach Sannidhanam (with 2 night halt in the forest). In those days it used to take even longer. The path is treacherous - walking barefoot on rocks, climbing and descending steep hills that stetches miles, encountering hot or rainy weather, taking bath in cold rivers, and eat whatever food you get. You need to be well-conditioned to undertake this yatra.
The mandala vritham prepares a devotee both physically and mentally for the journey. To that effect you're required to observe the following during vritham (and there's a reason for each one):
Ayyappa is a bramachari and is in a meditation pose in Sabarimala - you don't want to disturb him (hence girls above 10 years of age and women upto 50 years of age are not allowed to climb Sabarimala). That's good for Ayyappan, but what about people like us who need to move around in a society consisting of wife, sisters, daughters, relatives, co-workers in the above age? Since maintaining celebacy is of utmost importance, people who are in vritham withdraw themselves from the above group in 2 ways (1) by making themselves "unattractive" by not cutting/ combing hair, growing beard, nails etc. (2) letting the women know to stay away from them by wearing black/ saffron/ blue clothes, wearing mala with Ayyappa pendant, etc.
But is it possible to observe these in US? We need to temper it to make it practical. We can't go to work with unkempt hair or without footwear. It's okay to cut hair, shave, wear footwear (I've seen some Ayyappas announce in their work about the Vritham and grow a beard!). Outside of work, observe the austerities where possible - wear the black/saffron/ blue clothes at home, don't wear footwear at home (we don't do this even otherwise), don't shave during weekends, don't go to parties or others' houses (who are not observing vritham - they could cook meat in their home for e.g.), don't eat at restaurants (if you're not traveling), go to temple at least once a week, etc. The main requirement is for you to keep your mind pure by only thinking of God and work and nothing else.