Familiarize yourself with the music staff. Go on to www.teoria.com and click on Tutorials on the right. Then click on Reading Music. Under Reading Music section, read up on the Introduction, Reading Musical notes (the 12th down) and Accidentals. Without this basic knowledge, you can not comprehend what solfege is all about. Now go back to tutorials and read about scales.
Solfege is built on scales. Under Tutorials<Scales<Use of Scales, click on the Major Scale on the right side. Click on the little bell to listen to a C Major Scale. The names of the notes here are C D E F G A B C, but you would not sing that. Instead, there are syllable names that are used for all of the scales and they are: do, re, mi, fa, so, la, ti and do. Therefore, C is do, D is re, E is mi, F is fa, G is so, A is la, B is ti and C is do. Since solfege is particularly designed for sight singing music, the do is a movable do.
Click on the Scale Constructor under Scales and wait for it to load. Then, click on D and carefully listen to the D scale. Now, your do is not a C; now D is the do, E is the re and so forth.
Once you learn the basic concepts of music theory, you should start singing the solfege. First, use www.teoria.com's scale constructor. The scales on that scale constructor only are ascending, but it is fine for beginners. Start with an C, then click on the # above C, then D, then b about D etc. while singing along to the notes with the solfege. (If you click on any thing that does not make sense in music theory, the website just will not play the scale for you until you click on the correct accidental).
Once you master the major scales, which can take you from a few weeks to months to truly drill them into your mind, then you should move on to other scales such as minor and chromatic. However, be aware that the syllables of the solfege change a little bit for that purpose. You can learn more details on http://www.music.vt.edu/musicdictionary/appendix/scales/solmization/syllables.html.
Now sing the ascending scale do, re, mi, fa, so, la, ti, and do and sing it descending as well do, ti, la, so, fa, mi, re and do. You need to do this with every possible scale that you can.