Answer: The normal thing is to join all the notes with what they have in common - in this case that's the single beam of the eighth note - and then add short beams for the 16ths. The short beams should be inward, as illustrated below. The nice thing about beaming, as opposed to just writing flagged notes, is that the reader can clearly see the beat groups. Makes reading errors less likely.

That's the way Practica Musica or Songworks or Counterpointer will automatically beam the above notes if you choose them as a group and press the beam button. In 4/4 time or 2/4 time the above would have the value of one beat, so the musicians reading this can play it easily.

Cases might arise where you have to decide which way short beams will go. Again software will help with this, but since you have the power to override those choices it's good to know what would be right. For example, suppose you have 3/8 meter with an eighth note, 2 sixteenths, then an eighth. The software acting on its own would do it with the sixteenths grouped together, which is correct because it displays the nature of the 3/8 grouping: here are three things for you, an eighth, a pair of sixteenths, then another eighth. If you grouped these the second way it would sound just the same on the computer but it would be harder for a musician to read because now it looks more like two groups: an eighth note with a sixteenth, then a sixteenth with an eighth. If your meter were 6/16 that would make sense, but in 3/8 it's just confusing.

So, clarity for the reader is always the first goal. That is not to say composers don't sometimes ignore it. Witness this excerpt from the orchestra's rhythm in the Sibelius Violin Concerto, third movement:

Probably Sibelius had his own reasons for notating that the way he did. In fact, I'm sure of it; he means for the fourth note to be emphasized as if it were the first of a group of 3 in 6/8. But he's going to get that effect anyway, having indicated two upbows on the previous pair of notes. Making 3/4 look like 6/8 could mix up the viola section - the conductor is probably beating in 3 - and those of us who are not Sibelius might have better luck with the band if we notate this the second way. You can find more discussion of this topic on pages 16-17 of Exploring Theory with Practica Musica.