The logic of Venkatamakhi's system of Melas was described in the last few pages. For practical purposes, as a starting point, it is enough if you know the notes of a Melam (without a deeper knowledge of the logic) for singing or playing - especially if you are trying to play an instrument like Veena, Keyboard or Guitar. This page helps you to find out the notes from the Melam number or name and shows them on a keyboard and veena sketches.
But in Carnatic Music knowing the notes is only the starting point. You have to know how the notes are held - with or without Gamakam and what type of Gamakam, how important is that note in that Raagam and what the typical phrases of the Raagam are. The Raagam module of Rasika software (works in Windows OS) gives detailed explanation of the manner in which the notes are sung in 111 common Raagams with audio visuals showing Aarohanam and Avarohanam on a keyboard sketch and audio visuals of typical phrases of the Raagam. The software may be downloaded here or here. 75 Raagams of the Raagam Module with a similar interface rendered as web pages can be seen here. A general idea of how a particular note is sung in a Raagam in a given context can help sing from notation even if you have not heard the song before.
For a listener who is not interested in singing but wanting to identify the Raagam a knowledge of notes may not be required for well known Raagams which he identifies by intuitively comparing with typical phrases of known compositions. But in the case of less known Raagams he finds that some phrases are similar but the music sounds different. If the listener can identify which part of the octave the phrases lie - lower part (Poorvaanga) or upper part (Uttharaanga) and to which Raagam they sound like, he can combine them and get an idea of the Raagam (such as Purvaanga like Kalyaani(click to listen) and Utharaanga like Simhendramadhyamam (click to listen he may understand that it is Lathaangi (click to listen) which differs from the 2 Raagams only in one note in each case.) Sometimes a single phrase of a Raagam is so characterestic that even without covering the octave it could be identified - like da pa maa ga ri sa of Begada. A combination of these approaches (identifying phrases, identifying in which part of the octave they are sung and identifying notes) can give a full understanding of the less common Raagams.
The ability to recognise notes is called 'Swara Jnyaanam'. If notes are sung without Gamakams, it would be easy to develop Swara Jnyaanam but in Carnatic music most of the time the notes are held with Gamakam. A brief description of Gamakams is given in the next page.