Good question Bruce,
Personally I’ve been thinking about this and ultimately it’s up to the community.
So, how can you attract more users?
- Point out the growth Uniswap has seen recently, the recent developments & the major fact there’s now Uniswap Governance (fueled by the UNI token).
- Word of mouth will be valuable. Share your experience, point out the things you like about using Uniswap, because chances are, others would like these same things.
2.05B in liquidity, $500M+ daily volume, 9,600 pairs, fees distributed to liquidity providers, these are pretty hard to ignore for a lot of people 
Top of that, I’m sure the community will come up with great proposals to distribute UNI to more community members. Which would (hopefully) also attract a lot of new users.
Just my personal thoughts!