A character sketch is a piece of writing that carefully describes a character for a reader, including who the character is and specific details we know about the character from what the author wrote. When writing a character sketch, one first wants to complete a character analysis. When analyzing a character, what we are looking at is how the author presents the character as a person; we are looking at the character's characterization. There are many different things we can look at to analyze characterization ("How to Write a Character Analysis"). A few things to consider are that we want to pay close attention to the things the character does and says. We also want to think about the character's motives for actions--does the character have benevolent motives or non-benevolent? It also helps to look at the ways that other characters respond to the character. The things that other characters think and say about the character in question can help us understand a great deal. Below are a couple of ideas to help get you started.
Touchstone, like most of Shakespeare's fools, plays the role of a very intelligent court jester. In fact, most of Shakespeare's fools are ironically more intelligent about themes and situations than the other characters. Touchstone is no different in that literary critics have pointed out how Touchstone accentuates the values of the play through comedy (Palmer, "Touchstone"). Specifically, critic John Palmer asserts that "Touchstone puts all things and every person in the play, including himself, to the comic test ("Touchstone"). He puts the whole idea of escaping to Arden to the test by pointing out the foolishness of leaving comfort to be in a forest on the pretense that it is the better place to be, as we see in his line, "Ay, now am I in Arden: the more fool I; when I was at home, I was in a better place: but travellers must be content" (II.iv.16-18). He even puts Silvius's love for Phebe to the test by pointing out that love is mortal, meaning that it can die, and that all who love are foolish. Furthermore, while he is cynical about life in the forest, which he says is not as good as life at court, he also enters into an argument with Corin that, contrary to what Touchstone set out to do, actually contradicts his own cynicism and proves that country life is good on its own terms. Beyond putting everyone to the test and showing what foolishness exists, he also proves to be a very loyal servant in the fact that he very willingly follows Celia and Rosalind into the forest.
Hence all of these ideas and more would be excellent things to describe in a character sketch.