MIA49 is the Miami sector 49; VJ592 is ValuJet flight 592 (callsign "Critter").
MIA49: Critter 592, contact Miami Center on 132.45...so long.
MIA49: Critter 592, contact Miami Center on 132.45.
VJ592: Ahhhh, 592 needs an immediate return to Miami.
MIA49: Critter 592, roger, turn left heading 270, descend and maintain 7000.
VJ592: 270, 7,000, 592.
MIA49: What kind of problem are you having?
VJ592: Smoke in the cockpit...smoke in the cabin.
[Likely there were portions (or silence) removed from the tape at this point, for clarity].
MIA49: Critter 592, when able, turn left heading 250, descend and
VJ592: 250, 7000.
MIA49: [on interphone] Winco, 49. Winco, 49.
MIA49: Yea, Critter 592 is coming back to Miami, he's got an emergency...Eagle 703 wants 12,000 as a final.
WINCO: All right, thank you, SC.
VJ592: Critter 592, we need the closest airport available!
MIA49: [D-side overheard coordinating?: "...703"] Critter 592, they're gonna be standing by for you, you can plan runway 12...when able direct to Dolphin now.
VJ592: We need radar vectors!
MIA49: Critter 592, turn left heading 140.
[more audio likely removed here]
MIA49: Critter 592, keep the turn around, heading 120.
AAL1462: American 1462, we're passing 2 for 5.
MIA49: American 1462...roger.
[Transponder (i.e. mode C altitude readout) was lost around this time]
MIA49: Critter 592, contact Miami approach on... correction, you just...just keep on my frequency.
MIA49: American 960, turn left heading 270, join the WINCO transition.
AAL960: Heading 270 to join the WINCO transition, American 960.
MIA49: Eagle 703, contact Miami Center now on 132.45...Critter 592, you can turn left heading 100 and join the runway 12 localizer at Miami.
[Radar contact lost]
MIA49: Critter 592, descend and maintain 3000...
MIA49: Critter 592, Opa-Locke airport's about 12 O'clock and 15 miles...