In learning essential jazz guitar basics, you must have a grasp on the sound of jazz guitar. While there is no one definitive "jazz guitar sound," there are some general guidelines that jazz guitarists have typically followed. As opposed to rock, blues, or pop guitar sounds, jazz guitar typically has a warm, clean sound with little distortion. That's not to say that jazz guitarist don't ever crank it up - players like John Scofield can use overdrive and even distortion with subtlety and style without betraying their jazz roots, but historically, the sound of jazz guitar strives to emulate the tones of players like Wes Montgomery, Grant Green, Joe Pass, and so forth, and that means warm, clean tones.
Like other jazz instrumentalists, jazz guitarists, at least since the bebop era, tend to emphasize the relationship between the melody and the chord progression, i.e. "playing the changes" by emphasizing tones such as the 3rds and 7ths and other prominent extensions of the underlying chords. Jazz guitarists may utilize either alternate or legato-style picking, but also tend use such ornamentations as slides and grace notes. Again, emphasizing chord tones is crucial, particularly so-called "guide tones" such as the 3rd and 7th, and is an essential component of jazz guitar basics.
While the days are long gone where a jazz guitarist was expected to use a large archtop guitar with high action and flatwound strings, there are still some general guidelines that will help a player get a good jazz guitar sound.
You can get a get a great jazz guitar sound with many different types of guitars, including hollow body, semi-hollow body, and solid bodies. The key is to understand how to get a traditional jazz tone. If you're a fan of large bodied instruments, then guitars like a Gibson ES-175 can definitely get you in "jazz land" pretty quickly. Players such as Pat Methany, Wes Montgomery, Joe Pass, and Howard Roberts have all used an ES-175 at some point during their careers.
Personally, I favor a Fender Telecaster for my own jazz guitar work, and I'm not alone. Players such as Joe Pass, Mike Stern, Bill Frisell, and Ed Bickert have all favored Telecasters at one time or another. A Telecaster's neck pickup with a rolled-off tone control can get an excellent jazz tone.
Really, there is no one single "right" guitar for jazz - the Gibson Les Paul, Gibson ES-335, Gibson SG, and Fender Stratocaster have all been used by jazz players at one time or another. Bottom line - a good neck pickup with judicious use of the tone control can get you a respectable jazz tone, regardless of the guitar's body type.
Generally, jazzers will favor clean guitar amps, though there are exceptions (both Mike Stern and Al Di Meola have used high gain Marshalls at some point during their careers). Popular choices include the Roland Jazz Chorus (favored by players such as Pat Martino), Fender Deluxe Reverb, and the Polytone Brute series.
As far as effects, traditional jazz players will often eschew effects for a straight guitar-into-amp type sound, there of course there are many exceptions. Players such as Mike Stern and John Scofield are two such players who use effects as an integral part of their sound, and many jazz guitarists also use effects regularly, whether it's the reverb and chorus from the Roland Jazz Chorus or a more elaborate pedalboard.
Anyone who wants to play jazz guitar at even a basic level needs to have a working knowledge of essential music theory - chord construction, scales,modes arpeggios, and rhythm. Jazz players should also have a number of memorized phrases or "licks" that they can insert into their improvisation as needed. A good jazz guitarist also understands the phrasing and technique needed to establish a good sound.