Psallo, psallere is an interesting verb for an English speaker to work with, and doubly-so for a Catholic. Originally it means to play music on a stringed instrument, borrowed directly from the Greek. Greek especially is full of these weirdly specific action verbs, and Latin inherits more than a few. We don’t have anything like these in English, where the instrument gets its own verb (to piano, to guitar, etc.) or the sport gets its own verb (to football, to baseball, to cricket, etc.). For my translation purposes that poses a problem, since I try for as much formal correspondence as possible and hate multiplying words. The best we can do for the imperative is “play!” but that is awfully vague in English. You could try a monster like “instrumentalize!” or you could supply some extra words to make the sense plain. Annoying.
So that’s the first annoyance. The history of the Church does a funny thing to this verb, however. We call these liturgical songs “psalms” originally because they are psallere-d on a psalterium; i.e., they are named for the instrument used to play them. But thanks to monasticism and the historical practice of the Divine Office, these “guitar recordings” come to be chanted; i.e., sung without instrumental accompaniment. As a result the later use of the verb psallere–say, what St. Anselm would have meant by it–is just very simply to sing or chant a psalm. And in that sense, the most intuitive way for me to translate psallite is with the much clearer–but historically incorrect–“sing!”
“Omnes gentes plaudite” (Psalm 46)
 In finem, pro filiis Core. Psalmus.
Unto the end, for the sons of Korah. A Psalm.
 Omnes gentes, plaudite manibus; jubilate Deo in voce exsultationis :
All nations, strike with hands; rejoice to God in voice of exsultation;
 quoniam Dominus excelsus, terribilis, rex magnus super omnem terram.
for the Lord lofty, fearful, the great king over all the earth.
 Subjecit populos nobis, et gentes sub pedibus nostris.
He has thrown under peoples for us and nations under our feet.
 Elegit nobis haereditatem suam; speciem Jacob quam dilexit.
He has chosen for us His inheritance, the appearance of Jacob which He has loved.
 Ascendit Deus in jubilo, et Dominus in voce tubae.
He has ascended, God, in rejoicing, and the Lord in voice of trumpet.
 Psallite Deo nostro, psallite; psallite regi nostro, psallite;
Play to our God, play; play to our King, play;
 quoniam rex omnis terrae Deus, psallite sapienter.
for King of the whole earth is God, play prudently.
 Regnabit Deus super gentes; Deus sedet super sedem sanctam suam.
He will rule, God, over the nations; God sits over His holy seat.
 Principes populorum congregati sunt cum Deo Abraham, quoniam dii fortes terrae vehementer elevati sunt.
The princes of the peoples have been gathered with the God of Abraham, for mighty gods of the earth violently have been lifted up.
v. 8 sapienter This is a great double-entendre in Latin. The go-to definition for the word is wisely, and suggests that we are wise to play to the King of the Universe. It can also mean skillfully, and that corresponds better with what the Septuagint is doing here. He’s the King of the Universe–play as well as you can! Each of those options obscures the double-entendre so I had to dig a little deeper for something in English that can support both. Judiciously and prudently seem to do the job, but it kills me to use Latinates that aren’t really synonyms in Latin. Again, this is why we learn Latin–so as not to betray the words. Think of the poor words!
v. 10 dii Again?! Another double-entendre two verses later? Aiee! This word, marvelously, can be translated as “days” or “gods.” Might days have arisen? Mighty gods? Either one can work pretty well here. Complicating the issue somewhat is the Greek, which actually has something like “the mighty ones of God” have arisen. That tips the balance in favor of dii as gods here, with the added benefit that dii fortes terrae forms a nice parallel with principes populorum. The drawback is that a parallelism is not clearly called for here, since we are inside an explanatory clause (quoniam), and it’s not entirely clear that either gods or days does a better job explaining the main clause. My preferred sense for now is that dii fortes is a predicate of principes populorum–for they have been lifted up as mighty gods of the earth. Or something.