Strap on a single-cutaway Les Paul TV model guitar, so named for its honeyed-yellow finish, which--with various exceptions, dictated by circumstances--became the dominant model throughout his career. Associates like former Dolls soundman Nitebob assert that Thunders made this choice, because he was "too much of a klutz" to deal with more than one pickup switch. The Les Paul TV's setup eliminated those problems, featuring only one pickup, one tone and one volume control, respectively.
Make overdrive and volume an essential part of the equation, but resist the urge to slather the sound in distortion. Unlike his contemporaries, Thunders plugged straight into his Fender Twin Reverb "blackface" amplifier, with no effects boxes or pedals--presumably aided by the TV model's denser wood routed for the single P-90 "soapbar" pickup. To get his classic "squeal," simply turn up the amplifier as loud as you can stand it, and fire away.
Keep the chord changes simple and direct--if you're paying tribute, three or four will suffice. "Personality Crisis" is among the best-known examples, built around a powerhouse C-D-G sequence. This provides ample room for a lead guitar player to stretch out, without wandering from the basic framework. The elemental simplicity of '50s and '60s rhythm 'n' blues, soul and Top 40--sounds on which Thunders and his Dolls colleagues grew up--should not be underestimated here.
Form your playing style around simple, two-fingered power chords--a trick that Sylvain credits teaching Thunders early in the Dolls' career--and some well-placed string bending. Bend upwards toward the fret, using the inside string of the power chord that you are creating. For relevant snapshots, listen to the live version of "Chinese Rocks" from the Heartbreakers' "DTK" live album, or the stop-and-start dynamics of "Subway Train"--New York Dolls and solo versions.
Make sure that your Les Paul TV guitar is a double cutaway model, which is easily distinguished by the two "horns" on either side of the neck. This quality is essential for accessing the higher frets, and one that you will need to approximate Thunders' trademark screaming high-end approach.