How do I find out how old this is?
Hi Somer85,
Welcome to the forum !
Carbon14 is a very professional way of placing objects in time but not very accessible 
but maybe some other members may remember similar unicycles to give a rough estimate.
As for the value, it is mainly good to ride around or learn with. Then to a tiny extent, may be a good memory for those who learnt on one. But it is only worth its weight in scrap $$-wise.
considering the lollipop bearings and the cottered cranks that thing must be very old and of very little value
Carbon-14 dating is only accurate for items that are thousands of years old. It couldn’t even place that unicycle in the correct millennium. John Foss can date it much more accurately than that. I didn’t even know that UniVega had a unicycle line but apparently they still do. Ask them.
The pedals alone should tell you that it wasn’t a quality uni even back in the day, and it certainly isn’t worth much if anything today.
Knock-off of Miyata’s design, probably from the 80s. Value only as a curiosity.
Much has already been said about the unicycle’s value. I think it‘s an ok uni to learn but as soon as you want to do some tricks it won‘t be rugged enough. Given how cheap used unicycles can often be had this one really shouldn‘t cost much.
@ernst could you elaborate why the lollypop bearings are inferior, please? Is it because of the way the lollypops are attached to the frame in this particular case, or is it an inherently inferior design? For over 30 years I had a uni with lollypops, but the lollies were inserted into the cylindrical frame ends rather than bolted to the hammered frame ends like here. I think the design of my uni was a bit better / more rugged than the unicycle the OP inquired about.
There are two styles of bearing holders which are lollipop-shaped. This Miyata style, where the fork ends are stamped flat and the holders attached with a bolt, are fine. The style where the fork ends are cylindrical, with bolts through a cylindrical bearing holder inserted into the end of the fork, would eventually break. The fork itself wasn’t strong enough for the forces.
thanks, @tholub. So I got it the wrong way round, which lollypop style would be more durable. Me never having any troubles with the bearing holders probably just shows that I didn‘t ride my old uni hard enough 
Not exactly. It’s a Miyata, circa 1982 or so. I have two of them, but of the “Flamingo Deluxe” variety. Univega is a re-brand, but the ones I have are 100% Miyata except for the stickers! So it’s a good, solid 20" uni, and should take plenty of abuse within the range of square-taper axles. 
Cottered cranks makes it substantially less solid than square-taper would be.
D’oh! That does make it an older one, and less desirable. Still fine for a smaller human learning to ride, messing around, etc. But not a lot of jumping. Not sure when the non-Deluxe Miyatas changed to square taper…