Exegesis:

kai parachrēma aneblepsen ‘and (as a result) he recovered his sight at once.’

kai ēkolouthei autō doxazōn ton theon ‘and he followed him glorifying God.’ The imperfect tense is durative. For doxazō cf. on 2.20.

pas ho laos idōn edōken ainon tō theō ‘when they saw (it) all the people gave praise to God.’ For pas ho laos cf. on 3.21. The aorist tense of edōken refers to the immediate reaction of the people as contrasted with the lasting reaction of the healed man. edōken ainon is virtually equivalent to ēnesan (from aineō, cf. on 2.20).

Translation:

And followed him is usually better rendered as a new sentence. The verb here has the meaning ‘went with him,’ ‘accompanied him.’

Glorifying God, simultaneous with the preceding act: and, as he went (or, while he did so) he glorified God. For to glorify see on 2.20; An American Translation and Good News Translation render “giving thanks to God”.

For all the people cf. on 3.21.

To give praise to God, or, ‘to praise God,’ closely synonymous with ‘to glorify God,’ cf. on 2.20. If no suitable synonym is available one may say, ‘praising God—they too praised God.’

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.