A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 42:1Maschil--(See on Psa 32:1, title). For, or of (see Introduction) the sons of Korah. The writer, perhaps one of this Levitical family of singers accompanying David in exile, mourns his absence from the sanctuary, a cause of grief aggravated by the taunts of enemies, and is comforted in hopes of relief. This course of thought is repeated with some variety of detail, but closing with the same refrain. (Psa 42:1-11)
Compare (Psa 63:1).
panteth--desires in a state of exhaustion.
psa 42:2appear before God--in acts of worship, the terms used in the command for the stated personal appearance of the Jews at the sanctuary.
psa 42:3Where is thy God?--implying that He had forsaken him (compare Sa2 16:7; Psa 3:2; Psa 22:8).
psa 42:4The verbs are properly rendered as futures, "I will remember," &c.,--that is, the recollection of this season of distress will give greater zest to the privileges of God's worship, when obtained.
psa 42:5Hence he chides his despondent soul, assuring himself of a time of joy.
help of his countenance--or, "face" (compare Num 6:25; Psa 4:6; Psa 16:11).
psa 42:6Dejection again described.
therefore--that is, finding no comfort in myself, I turn to Thee, even in this distant "land of Jordan and the (mountains) Hermon, the country east of Jordan.
hill Mizar--as a name of a small hill contrasted with the mountains round about Jerusalem, perhaps denoted the contempt with which the place of exile was regarded.
psa 42:7The roar of successive billows, responding to that of floods of rain, represented the heavy waves of sorrow which overwhelmed him.
psa 42:8Still he relies on as constant a flow of divine mercy which will elicit his praise and encourage his prayer to God.
psa 42:9in view of which [Psa 42:8], he dictates to himself a prayer based on his distress, aggravated as it was by the cruel taunts and infidel suggestions of his foes.
psa 42:11This brings on a renewed self-chiding, and excites hopes of relief.
of my countenance--(compare Psa 42:5) who cheers me, driving away clouds of sorrow from my face.
my God--It is He of whose existence and favor my foes would have me doubt.