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 86:1This is a prayer in which the writer, with deep emotion, mingles petitions and praises, now urgent for help, and now elated with hope, in view of former mercies. The occurrence of many terms and phrases peculiar to David's Psalms clearly intimates its authorship. (Psa. 86:1-17)
poor and needy--a suffering child of God, as in Psa 10:12, Psa 10:17; Psa 18:27.
I am holy--or, "godly," as in Psa 4:3; Psa 85:8.
psa 86:4lift up my soul--with strong desire (Psa 25:1).
psa 86:5unto all . . . that call upon thee--or, "worship Thee" (Psa 50:15; Psa 91:15) however undeserving (Exo 34:6; Lev 11:9-13).
psa 86:8neither . . . works--literally, "nothing like thy works," the "gods" have none at all.
psa 86:9The pious Jews believed that God's common relation to all would be ultimately acknowledged by all men (Psa 45:12-16; Psa 47:9).
psa 86:11Teach--Show, point out.
the way--of Providence.
walk in thy truth--according to its declarations.
unite my heart--fix all my affections (Psa 12:2; Jam 4:8).
to fear thy name--(compare Psa 86:12) to honor Thy perfections.
psa 86:13The reason: God had delivered him from death and the power of insolent, violent, and godless persecutors (Psa 54:3; Eze 8:12).
psa 86:15Contrasts God with his enemies (compare Psa 86:5).
psa 86:16son . . . handmaid--homeborn servant (compare Luk 15:17).
psa 86:17Show me--literally, "Make with me a token," by Thy providential care. Thus in and by his prosperity his enemies would be confounded.