Is there a way to hook up a solar power panel to a small appliance?

Sure you can use a solar panel and dump the output into a bank of 12V batteries as an example. However, you need an inverter which converts the 12DC into 120VAC so you can run your toaster. The cheaper/cheapest inverters give you a simple (bipolar) square wave. using a switching transformer. Then there are the ones who have a stepped waveform (4 steps being the minimum with a distinct zero portion) and the very expensive ones deliver a sine wave. The latter is basically a DC amplifier with a 60Hz sine oscillator driving the power section. The sine wave can also be derived from a digitized signal with various numbers of steps.

EDIT: I assumed that anyone using an inverter knows that one can not power a 500W microwave with a 100W inverter.

You need a solar panel adequate to collect the energy the appliance needs, plus an inverter (also of adequate capacity for the appliance), and you need to account for losses in the inverter. It is recommended you also have a method to store the energy, usually a battery of some sort.

Typically, those mentioned appliances are intermittently used, and as such a smaller panel could be used to charge the battery over the day, the appliance drawing the power off as needed. Also, to reduce demands on the system, you should get as efficient appliances as possible, including ones that don't draw "phantom" power, or disconnect them from power when not used.

You need an inverter to convert the DC out of the solar panel into the AC those appliances use. You can buy these online, but you need to size the system parameters (volts, amps, watts). The panel should say how much it is putting out, it will be x VDC or volts direct current. The inverter will have parameters on how much it can put out. Standard household electric in a house is 120VAC at 60hz, and for most kitchen appliances you should make sure the inverter is rated for 20A.
You need to be getting enough power out of the solar cell to power an item like that. Coffee makers and microwaves are high power items so that may be a little ambitious. You might want to start with a clock radio or something else small like that.
It might also be helpful to experiment with some battery powered things first, those are DC to begin with so you don't need the inverter, just enough volts to power the thing and to figure out the wiring.

Invest in Photovoltaics: Design and Installation Manual, by Solar Energy International. Its the definitive manual for this sort of thing.

No,

A 700$( 2 foot x 5 foot) panel only produces about 5 amps @ 12 volts dc (nominal)

this equals 60 watts- (power = power i.e 12×5= 60 watts= 110x .5= 60 watts), A coffee maker takes about 600- 1500 watts! Besides you would need to convert 12vdc to 110 vac with and inverter which will cause at least a 10% power loss.

That is why the system is panels- batteries- inverter, and alot of them in 100% full sun, to power small appliances only for a short period of time.

Makes you realize how the lies about powering our country by solar are just propaganda.

While there are ways to make such an arrangement work, there would be practical issues. Cheap panels are likely to be low-wattage, and you would probably need to stack several of them to get enough voltage to power a coffeemaker – although you could probably hook it up without an inverter. It would be costly, and inefficient.

If your end goal is hot coffee, consider getting a solar water heater or solar oven. That will give you boiling water at 1/10 the cost of electric panels, maybe 1/50 if all you want is one cup.

Many suggest to use an inverter (to go from 12V to 110C AC) but its a bad idea, there's many losses in conversion, it's not elegant

It's better to get 12V applicances, like camping style, then just hook them to your SP or your battery (make sure enough amps)