Q:

What is the easiest way to hook up a monitor speaker without needing a mixer?

How would you normally connect another speaker to an existing speaker (ie. guitar amp) in order to use it as a stage monitor?  Does the speaker need to have some special output like 1/4 trs or xlr, which goes to the other speaker?  I am a little out of touch on the requirements involved here.
I am basically looking for a simple solution for small gigs, where I would have my main guitar amp facing the crowd, and a monitor pointing at me (so I can hear myself better).

A:

You've got two ways to do this, with a passive external speaker or a powered one.
In the first way, the guitar amp is driving both speakers directly.  If you have a seperate amp and speaker cabinet there may even be a pair of output sockets.  There may also be a warning - 'total load not to exceed 4 ohms' or something.  Heed the warning!  If the second speaker is designed specifically as a passive monitor, it may have a volume control.  Otherwise the volume balance between main and monitor speaker will be out of your control.
For this, and other reasons, it's better to use a powered monitor.  Feed it from a Line Out socket on the main amp.
Also consider this. Guitarists often position their amps to beam sound straight into the audience's faces, and into the back of their own knees. This actually annoys everyone.  Consider pointing the amp more at the person who WANTS to hear a lot of it - you, the player.  This will probably make you turn your volume down a bit too, which will please everyone.   

A:

As long as you are talking about using an ancillary speaker cabinet as a stage monitor for just your GUITAR amp output, (and not the total band mix including vocals) then it's quite easy;
First, you examine the back of your guitar amp to see if it has a 1/4 jack output for sending the guitar signal to a second speaker. Many amplifiers offer this feature, and the output jack lists the wattage and ohms requirements for that other speaker. It may be labeled OUT, LINE OUT, or EXT SPEAKER.
It's not recommended to use the EFFECTS OUT jack for this purpose, because the output signal is quite low, and plugging a cable into that jack may defeat the amp's main speaker output altogether (anticipating that there will be an EFFECTS IN plugged in in order to complete the loop).
Use a standard guitar cable to chain your amp to that speaker, and take the time to check your stage volume versus monitor volume. Don't forget that the drummer (if you have one) needs to hear your guitar sounds just as much as you do, so speaker placement is paramount. 
I have seen players chain to a small ancillary speaker by using standard two-strand speaker wire and two pairs of alligator clips, and connecting the amp speaker tabs (+ and -) to the 2nd speaker's tabs. This is sort of a cheesy solution, but it certainly gets the job done, depending upon your stage requirements and traffic. 
Good luck!! 

