Thaalams now in use have 3 Angams or parts called the Laghu, Dhrutham and Anudhrutham (except in the case of 'Chaapu thaalams').
The Angams are defined by the manner in which the rhythm is kept by hand movements (Kriya). Rhythm is kept by beating or clapping with the palm, counting with fingers and waving (or turning up) of the palm. A Laghu consists of a beat followed by certain number of counts depending upon the Jaathi of the Thaalam. A Dhrutham is a beat and a wave while the Anudhrutham is simply a beat.
Normally the beginning of each of the Angams represented by the beat is also the point of accent. The time interval between any of these actions has to be constant and each action is an Aksharam. The units of time for a dhrutham is always 2 and for anudhrutham 1, but the number of units for the laghu will depend upon the jaathi of the thaalam. The hand movements help in keeping rhythm of complex thaalams like the Ata thaalam having 4 angams with a total of 14 aksharams in a cycle.
The popular 'Aadhi' thaalam consists of 8 aksharams in a cycle divided into a laghu with 4 units followed by 2 dhruthams of 2 units each. Thus for the laghu (4 units) the singer claps once and counts 3 times with fingers, and for the 2 dhruthams he claps , turns the palm up, again claps and turns the palm up to complete a cycle. You can see a pictorial representation of Aadhi thaalam and hear beats. See how a song (2 lines of Vathapi in Hamsadhwani) is fitted into the rhythm cycle. Note that although the lyric starts with the rhythm cycle, the aksharam positions do not always coincide with the consonants (the 'thaa' and 'pi' in 'Vathaapi' and more).