Karthika masam starts on the day after deepavali and ends after 30 days.
Here i am giving the basic rituals we should follow for this month. You can find the detailed vratha vidhanam in karthika puranam book.
1) One should not eat non veg food for the whole month.
2) Must take meal only once per day for the 30 days, we can eat breakfast at nights or atleast we must follow this on auspicious days like mondays, karthika poornima, koti somavaram etc.
3) Must take shower(including hair) daily.
4) Must light deepam every evening and do pooja.
5) Read one chapter in karthika puranam book everyday. If you don’t have karthika puranam read the story given in the below link daily http://www.teluguone.com/bhakti/shivastutulu/index.jsp?filename=kartika.htm
It is even good to hear the story if someone is reading it loud
6) Prepare prasadam on mondays , karthika poornima, koti somavaram and remaining days you can even keep some fruit as prasadam.