I have a desk fan that has three speed settings. It is not a Ceiling Fan so a fan control switch is not an option here. I tried placing it on a wemo mini switch but the toggle of on and off did not work with the fan.
Does someone know of a work around?
Hard to know without knowing what fan it is and what the switches look like, but our desk fan work fine with standard wall switches, you just need to leave them in a one of the 3 fan settings. I agree it would be better to have full control of fan speed, but that is quite a lot more complicated to engineer, needing 3 different relays which cannot be on at the same time without causing problems.
We have fans that we use as white noise for the kids when they sleep. 3 speeds too. I have them plugged into Aeon Labs Smart Energy Plugs and it works fine.
https://www.amazon.com/Aeon-Labs-DSC06106-ZWUS-Z-Wave-Energy/dp/B007UZH7B8
BTW, at first glance I thought… who’s not a fan of desks?
It just depends on the specific fan model. There are three options for automating a desk fan.
1. Use a smart plug-in module with a fan which returns to its last state when power was cut
For this option, you need a fan model which will return to the “on” state when power is restored.
That is, if the fan is plugged in and turned on, so that the fan blades are moving, and you unplug it And then you plug it back in, will the fan blades start moving again when the power is restored?
Some fan models will do this, but some have an automatic shut off when the power is cut and so when power is restored the Fan blades won’t move until you push a button on the fan again.
If the fan blade start moving again when power is restored, you are all set for on/off Control. ( you won’t be able to change the speeds with this approach, however.) You can use any pocket socket that smartthings can control. 
2. Fans with an IR remote
If the fan has the automatic shut off feature, but it also has its own handheld remote and that remote uses infrared (IR) then you have some additional options. You can use a Logitech Harmony, which is great if you happen to already have one operating in that room. That’s the easiest one to integrate with SmartThings, because there’s an official integration. You can probably use a Zmote. You can use Broadlink, although that one has a more complex set up.
There are a number of other IR blasters where integration may be possible although the set up can be technical and may require an additional device or an android phone. So it can be done, but almost all of these would be overkill just for desk fan.
The one that people most often have already but don’t realize it can be used for this purpose is the Logitech Harmony.
3. Naran Push Microbot
Another retrofit option which works well but is expensive is the Naran push microbot. This is a “robot finger” which is just a tiny battery powered actuator which has its own Wi-Fi bridge so you can use it with IFTTT.
I use these in my own home because I am quadriparetic and have limited use of my hands. This just solves some problems that nothing else will. For example, I have a mini blender. I can put the container on the blender stand and the top on the container, but I can’t push the button on the blender. The microbot does that for me. 
I also have an old VCR which I really like, but the eject button has to be physically pushed on the front of the unit. So I have another Microbot there. Another community member put two of these on a pellet stove, one for on and one for off, and so automated that.
The point is just that if you just need a button pushed, whether it’s on a remote control or on the device itself, the Naran system is A fast and easy way to automate that without having to rewire the device in anyway. But the microbots cost $49 each. And the bridge (one Bridge can handle about 40 microbots) is another $80. So it’s good to know this solution exists, but most people will go with something else. So I mention it just for completeness.
Could you list the brand and model of the fan? That’s usually the critical factor, since some fans will return to their previous state when power is restored, but other fans have a safety shut off. You can’t always tell just from the product descriptions which fans are which.
I will when I get home, but they’re just cheap fans from Wal-Mart/Target or somewhere. It has a physical switch to change the speed.
It’s usually the less expensive fans that don’t have the auto shut off, and so are better for this purpose. 
But it just varies from model to model.
Yes, sometimes simple is better.
I’m 99% sure this is the fan.
https://www.walmart.com/ip/Honeywell-Table-Air-Circulator-Fan-HT-900-Black/16503230