A tale of two performances
Remember the days, when you showed your friends Forward Pass and Rock the Baby and everybody went "Oooohhh"? Add Double or Nothing and Walk the Dog and the audience was convinced, that you are a yo-yo wizard, despite just using a five dollar fixed axle yo.
Then one day you got yourself a hyper unresponsive high end hundred dollar thingie and started to learn all those fiendishly difficult string tricks. Back out in the street you show the kids Kamikaze, Kwijibo, White Buddha, And Whut. The response? "That's nice. But can you show me Rock the Baby again?" No kidding, it happened to HB, and probably to many others as well.
Effect and audience
So, what is the key to a good yo-yo performance. Actually there are two keys, the audience, and the effect of a trick. Let's start with the latter.
If you look at the four last tricks, you will notice, that they are all sidestyle string tricks. To the layman audience the effect of all four is "He can toss the yo-yo from side to side in a string formation." It is the same for all four tricks. The first performance, however simple the tricks may be, contains four very different effects: "throwing to all sides", "depicting a cradle", "complex string formation", "rolling the yo-yo around and still having it return". The effect is what makes yo-yo tricks recognizable for a person.
In the last paragraph, we spoke about a lay audience. To a crowd of seasoned yo-yo players, the effect might be completely different. They might think "all old stuff" about the first tricks, but look at the four string tricks with different eyes. To them the effect might be "That magic drop sure looks good.", "And whut was that move, that got him into the second green triangle?" The example shows, that the effect of a trick depends greatly on the audience.
So, when deciding what to show, try to figure out what the effect of a trick is for your audience, and show them lots of different effects.
Getting and keeping attention
To keep your audience's attention, little surprises can help. This gives the onlooker the feeling that he is going to miss something, if he looks away for a second.
Example: Start a performance with a little story:
"Last week I bought a yo-yo for my kid and decided to try it out. Guess what, the darn thing did not work." (throws a sleeper)
"It does not come back. What kind of yo-yo is that?" (picks up the yo-yo, clumsily winds it again)
"I tried again" (throws a long sleeper)
"Only then I found out..." (tugs on the string with his free hand, like strumming a guitar, yo-yo zooms instantly back to his hand)
"...you have to tug on the string to make it come back."
The very second the yo-yo comes back, the audience is surprised. This surprise is amplified by the clumsy first throw, which left the audience thinking "Oh dear, what a klutz." Surprises like this can spark curiosity in an audience.
Every surprise is a little climax in your performance. Also try to add an overall climax by starting with simple tricks and progress to something (at least perceived to be) more difficult. If you start a performance with a Double or Nothing, nobody is going to find a sleeper spectacular anymore. Make sure, you really master those final tricks. Nothing can ruin a performance like a fumble during the grand finale.
Let them yearn for more
When performing magic, the rule of thumb is "Always give them one trick less, than they want." Even as a good yo-yo player, it will be difficult to be entertaining for more than ten to fifteen minutes. If you keep going past the point, where the audience is curious, they will become satiated. It is a bit like with vacation photos. Show someone one or two really good photos, and he will remember the experience as pleasing. If you show fifty photos, the person will probably never ask you again about how your holidays went.
Telling a story
Yo-yo tricks are usually quite isolated feats. By binding them together with a little narrative, it is possible to add a little "glue" to a performance. This opens up quite a number of interesting style elements.
As an example you can use a running gag, like rocking babies several times in a routine. The first "normal" rock the baby, is usually quite well received by audiences. When performing Man on the Flying Trapeze, remark "Oh, did you know? Trapeze artists also rock their babies, but never without a safety rope." (do a Trapeze Baby). A while into the performance, do Crazy Cradle and while tying the "web" say "And on a recent expedition into the Amazon jungle, researchers found out that..." (now do the rocking) "... some spider mommies also rock their babies.". Always gets a laugh and makes the audience wonder, what you will rock next.
As showing off with a yo-yo is similar in many regards to performing magic, the book "Magic and Showmanship" by Henning Nelms contains lots of good advice.