How do I remember quotes from articles in my exam?

The best way to do this is to dedicate a page (or whatever materials you use to revise) for each theme, and pick two key articles for each theme. Make sure you really understand the articles- if you try to chose one that is too complex you will struggle to remember this in your exam! After reading the article, try to give a summary of it in your own words. By putting artiicles into your own words you are more likely to process the information!
It is important to note that in exams the examiner is not looking for perfect quotes from critics. Paraphrasing a quote/ knowing the critics general argument will be more impressive and helpful to your overall essay argument than misquoting a critic or 'throwing it in' for the sake of it.
Try and identify a couple of articles that can relate to many of the themes. For example, if you are analysing the characters and themes of King Lear, an article such as 'The Role of Edmund in King Lear' (McNeir, Vol 8) would perhaps be limited to just a character analysis of Edmund, whereas 'The Storm in King Lear' (Dunn, Vol 3) could be used for the theme of weather, blindness, power, stage directions and more.
A couple of staple quotes should be learnt that can fit most essay questions, finding an informative quote from an articule about Shakespeare's tragedies for example can be worked into most essays to show general knowledge about the play as a whole.