Example 1, One-way Chaos:
In play: Mishra, Artificer Prodigy and Possibility Storm.
In hand: ANY ARTIFACT, for this example, lets say everyone's favorite, Sol Ring
Step 1: Cast Sol Ring
Step 2: Two triggers occur; Possibility Storm, and Mishra, Artificer Prodigy's search effect for 'Sol Ring'. Place Mishra's trigger onto the stack first, then Possibility Storm's on top.
Step 3: Resolve Possibility Storm, ultimately putting the next artifact on top your library into play, and then all revealed cards, AND Sol Ring onto the bottom of your library
Step 4: Resolve Mishra's trigger, searching your library for a copy of Sol Ring to put directly into play. Pro-tip: its more than likely on the bottom. Put into play for free. PROFIT!
With this in play, your opponents never get the spell they want, where as you get 100% of your artifacts, AND a free artifact into play with it on EVERY cast. It's like cascade for us, while our opponents struggle with the loss of their hand. Do not underestimate the mind games that this will play on them.
Example 2, Counter me not:
In play: Mishra, Artificer Prodigy and any counter spell effect, lets say Nullstone Gargoyle
In hand: Sol Ring
Step 1: Cast Sol Ring
Step 2: Stack Mishra's trigger first, then the triggered counter spell effect on top.
Step 3: Resolve the counter spell, countering Sol Ring, placing it in grave.
Step 4: Resolve Mishra's trigger, search your grave for a copy of Sol Ring, put it into play for free.
Not only does this work well with your own symmetrical counter effects, but cards like blood funnel suddenly make all artifacts 2 less to play! Better still, this aids us against control decks, if the other blue players counter our stuff, it still goes into play! Assuming of course they are careless with the stack...