Where is the best place to start learning basic electronic/arduino control of 110v lamp/fan, etc.. Simply switching on/off as an electric switch do.
First off, what's your experience with household AC? The answer to that will indicate what we can advise you on. If you have -no- experience (wiring up a single lamp doesn't count), then I would suggest going down to your local big-box home-improvement center, purchasing a book on home electrical wiring and appliance repair, and studying that - before you try anything.
Nice big relay. Easy. Check the driving voltage, typically 12 volts, you should be able to switch 12v with a transistor then that can go to the coil of the relay which switches the larger current.
Household AC is not something to "play" with - it can kill you just for looking at it wrong. I can't tell you the number of times I've been "lucky"; she's a hard b*tch.

Nice big relay. Easy. Check the driving voltage, typically 12 volts, you should be able to switch 12v with a transistor then that can go to the coil of the relay which switches the larger current.
This can work, but you need to check the contact ratings and such to make sure that the relay can handle the current being switched. Otherwise, you'll end up with a welded or burnt-out relay in short order.
Also, don't forget the snubber/flyback diode across the coil of the relay if you want to see your transistor live long.
Another thing to keep in mind: large currents can be controlled via a multi-relay setup, where one relay switches 24 VAC, which is then used to switch what is called a "contactor" relay (its basically a really big relay - you see them used in industrial and HVAC situations). The 24 VAC is generally provided using a step-down AC transformer; this is basically how your home AC unit works.
Also - if you want absolute safety, use two SPST or a single DPDT relay to switch both legs (neutral and hot) of the AC line at the same time (this is how the old AT power supplies of PCs were switched back in the day - but using a DPDT button switch, not a relay). This is actually better practice than simply switching the hot leg of the circuit.
Instead of relays, SSRs (Solid State Relays) offer an easy alternative; most can be switched using 5V TTL signals (like the Arduino outputs on its digital i/o lines) - you may or may not need a current limiting resistor on the ouput; check the specsheet for the SSR on current draw. The main disadvantage of an SSR can be cost; they are typically much more expensive than a similar relay. You also will typically need to mount them to a heatsink if you are going to be switching large currents. The advantages, though, are longer life, less noise, and no contacts to burn out.
Finally - always incorporate a ground into your project (ie, the case of the project box holding the AC controls would work well). You should also isolate the AC side of things well away from the controller, perhaps also incorporating an optoisolator design, so that transients, spikes, etc have no way to come back to the Arduino side of things (this is one area where you -don't- want to tie your grounds together, if it can be avoided).
Be careful.
