Swadhyaya means self-study. It means to do regular Japa of our Ishta Devata and to have regular study.
Regular study of such books that sharpen the intellect and enhance capacity such as Viveka or discrimination about what is permanent and what is temporary. This in turn will help understand subtleties of situations and subjects thus helping either directly or indirectly in Atmadarshan.
While looking into Spiritual and Mundane, this has been already referred. The Viveka is a must in deciphering it properly. Swadhyay develops that Viveka.
Swadhyaya traditionally means Study of the Shaastras. This gives us a scale to evaluate our progress; otherwise we tend to justify our impulsive actions with our own logic. The test of Dharma of what is right or not is determined by the Shaastras. Regular study of the Shaastras is essential. Since we have several Shaastras; a question may come to mind as to which ones to read.
Many times when we read the Shaastras, the Sutra form or archaic language is difficult for us to understand and thus we have to take the assistance of some commentaries. For today's complexities and in modern scientific terms, Swami Vivekananda is one of those few persons who have explained Vedanta very lucidly by synthesising various philosophies. Thus we can get the essence of our Shaastras in today's language in the Complete Works of Swami Vivekananda.
Viveka develops through regular study and the Japa of our Ishta Devata helps us in realisation of Ishta Devata.