'D.C. Al Coda' is very similar to 'D.S. al coda', the D.C. part stands for 'Da Capo' (Italian for 'afresh'). The only difference with this version is that instead of jumping back to a segno, you jump back to the start of the piece. You will still get the 'to coda' and 'coda' marks discussed in the D.S. lesson, but the segno is unnecessary here.
Similarly, you may also see the note 'al fine' instead of 'al coda' (for example Da Capo al Fine) which is paired with the text marking 'fine', which is Italian for 'finish'. In this case you will jump back as you would have in either the D.S. or D.C. al coda markings but instead of jumping to a coda, you just play up to the bar that has 'fine' written above it and stop.
Below I have provided two short pieces of music, both using a lot of repeat marks. Have a look through and see if all the repetition makes sense then try playing the pieces.