As the word "sketch" implies, this term began in art, suggesting a drawing done quickly, to gather the most obvious impression of a person in a rough, immediate fashion. So, when applied to drama, the term character sketch, implies a quick description of a character, one that captures the character's most salient characteristics -- the character's essence.
Adam is the aging servant to Orlando and Oliver. He actually served their late father, but has determined to remain in service to his dear master's sons. So, off the bat, we know that he is loyal.
He is also generous, since he has managed, over his long life, to save a bit of money from his servant's wages, and he gives this money to Orlando when he decides to accompany him to the Forest of Arden. He goes with Orlando and deserts Oliver, because, though Oliver is the elder son, Orlando is more honorable. This indicates that Adam has a great deal of integrity, as well.
He also represents family love and honor, since his dedication to Orlando (even as his age prevents him from being the strongest of companions) remains constant throughout the play, and Orlando returns the familial bond in equal measure.
So, for a quick sketch of Adam, the elderly servant of Orlando and Oliver, he is: loyal, generous, acts with integrity, and exhibits a great capacity for family love and honor.
Just a side note: Since drawing and painting involves illustrating a character's external characteristics (how they look) and the drama involves illustrating or revealing the character's internal characteristics (how they behave and why), "character analysis" is rather a better term to use when looking for description of a character from a play than "character sketch." Characters in plays are played by many actors, who possess various physical attributes, so how a character looks is the least likely thing for a play to describe about him or her.
Enotes has a great 10 step process to "Writing a Character Analysis," which I have linked for you below.
Adam is one of the least people whom you can refer to as a protagonist in As You like It. He is ever so open and loving and is one of the most compassionate companions of Orlando. He gives an excellent starting to the play along with Orlando.
Initially, we find him as one of the servants or rather the “dogs” of Oliver, as Oliver calls him. But we also get to know in Act 1 Scene 1 itself, that Adam loathes the company of Oliver and loves Orlando a great deal. He is the person who protects Orlando and informs him about the vices of Oliver and how Oliver plots to kill him.
Later on, Adam altruistically gives all his chattels to Orlando and accompanies him to the Forest of Arden, accepting him as his master. He is one of those Shakespearian characters who advocate the message of honesty and care. Adam, although in a helpless and miserable condition, seeks no help from Orlando, in the Forest of Arden. He is ready to die happily without anything in return for his kindness - epitomy of gentlemanliness.
Dear master, I can go no further : O I die for food.
Here lie I down, and measure out my grave.
Farewell, kind master.
(Act 2 Scene 6)