Connect the notes together, make it smooth.
Everything comes in on downbeats, but it is in 3/4 so it has the waltz sort of feel to it.
You can check out a recent recordings of it if you would like, low and an octave up:
neal_tenor_cielito_8_8_14 (mp3, right click and save as)
neal_tenor_cielito_8_8_14_up (mp3, right click and save as)
Note: depending on your reed, low notes can be tough to get out! Esp. on tenor.