A mantra is a chant or a phrase used to focus the mind on "not thinking". Mudras as I know of them are body positions.
Keep it simple. I would find a comfy spot where you wont be disturbed. Sit in half lotus or seiza or a position which is comfortable for you.
Close your eyes and relax into your breathing. Focus on the in and out breath into your centre. Breathe deep into your belly - Buddhist sytle breathing please.
Dont worry about the chanting, it isn't necessary other than to dull the mind into not thinking. Empty the mind of thoughts, just be the breath.
If you can hold this for a minute the first day then go for 2 the next and so on. If u find thoughts straying then just focus back on the breathing and push the thoughts aside and acknowledge that you will deal with them later.
Focus. Breathe. Be.
You can find mantras for chanting and get CDs of chants from many places. I have a long CD of a zither just quietly humming which is amazing to meditate to.
Popular mantras are OM, Om namah Shivaya, On nami padme hum to name a few. basically anything will do as long as you can chant it.
I did a search and found some nice descriptions of Om mani padme hum http://easternhealingarts.com/Articles/mantra.html http://www.purifymind.com/OmManePadmeHum.htm http://www.dharma-haven.org/tibetan/meaning-of-om-mani-padme-hung.htm