Namaskaar Raman ji,
It is absolutly essential to be aware of the mathematics involved in Jyotish, we propose to deal with it seperately, but it may not be possible also, Jagannath alone knows.
We were thinking of giving the calculation of the Charakaaraka in a seperate lesson, but since everyone seems to be interested more in them we give the calculations below, in a nutshell.
The Graha with the highest Longitude in a sign (how far it has progressed in a sign) is the Aatmakaaraka,
the one with the second highest longitude will be the Amaatya Kaaraka,
Then comes the Bhraatru kaaraka, Maatru Kaaraka, Pitru Kaaraka, Putra kaaraka, Gnyaati Kaaraka and the Graha with the least longitude (Amsha) is the Daara kaaraka.
For Raahu the longitude will have to be counted in the reverse.

for example take the following longitudes in a birth chart:

Surya - PiK         12 Simh 14' 01.05"  
Chandra - BK        21 Meen 59' 37.86"
Mangala - PK         6 Tula 16' 20.36"  
Budha - MK          14 Simh 41' 59.21"
Guru - AmK          23 Simh 51' 27.03"
Sukra - AK          26 Mith 29' 21.57"  
Sani - DK            3 Kanya 33' 36.66"
Rahu - GK           25 Kark 32' 57.16"

Shukra is the Aatma Kaaraka because it has the highest longitude amongst the Grahas in any Raashi.
Same way for other chara kaarakas.
Raahu is placed in 25 degrees in Kark but if counted from the reverse (because He is always retrograde) it has travelled only 30 degrees minus 25 degrees = 5 degrees and hence has the Graha with the second least degrees in the Raashi and so he becomes the Chara Gnaati kaaraka.
we would advice becoming familiar with the Naisargika Kaarakatwa of the Grahas before going to learn Chara Kaarakatwa.
The list of the natural significations of the Grahas are endless and the more we get to know about it the more easy it is to read a Kundali.

RishiRahul and vivek.

Dear Vivek ji,
Thank you for replying and using a typical chart for an explanation . I have asked this question twice but it got deleted on its own from the forum....
i m not sure how.But it is nice to see its reply from you.One more question ;-)as far as i remember Amaatya means motherless(or soemthng like this) doesnt it ??If yes, has it got any particular role to play in its naming or its significance.If No... then im sorry for this idiotic question.

Thanking you
Raman

Namaskaar Raman ji,
Amaatya means an Advisor or in olden times the cheif minister to the king. He is the second in command (the Aatma kaaraka is the King).
This shows the importance of the Amaatya Kaaraka in a horoscope, this also shows the importance of brushing up your Sanskrit.
RishiRahul and vivek.

Namashkaar Ramanji,

Amaatya means "ministers, counsellors of a king, inmate of the same house, belonging to the same house or family, a companion (of a king) "', minister.

An explanation:Amatyakaraka
The graha obtaining the second highest longitude is called Amatyakaraka. It signifies the mind. Its role is that of a Minister who guides the king, the Atma. It is the Amatyakaraka who guides the destiny of the person towards attainment of the desires of the atma. It is the protector of the soul.

Where did you find the'motherless' expression?

In astrology means career.

No question during learning is idiotic. It is a learning process; unless it is intentionally made.

Vivek and RishiRahul

Dear Rishirahul and Vivek ji,
Thank you for replying to my question.And Rishi rahul ji it is nice to see you back to the academy.
Actually i have never learned Sanskrit :( never got chance to do so.Though i recently was thinking
to learn it though i have not got any major purpose to do with it but i just felt like that i should give it a go
if god and time permits.
Vivek ji and Rahul ji,I have read that meaning of word "Amaatya" from a book (or an e-Book) a while ago.
I dont remember the actual source but it was mentioned there that Amaataya means motherless or not from
the same mother(something like this only)But anyway thank you for guiding me.

Once again thank you.

Regards
Raman