Get an adapter. I don't know where since Radio Shack went out of business.
Buy a speaker wire level cable that has two 3.5 mm on it. Then cut one end off. One issue, you need to get the phasing right. Phasing for speakers is they all push their cones out at the same time when all are playing one frequency. This might not be an issue with the sub but you should probably wire it the same way as the regular speakers.
Have a local expert help you in person.
Sounds like you have a "passive" sub (no power cord - no amp built in). If so then you would connect it to the receiver the same way as before. Connect it to the right and left speaker outputs. You may need to adjust the surround settings to get something that works.
That's a new one on me. Theater receivers have a coaxial, (or RCA form) looking output for their LFE (bass preamp) output, a single jack. There can be two of these on X.2 type receivers, obviously) Quite old video cards do use pin jack outputs usually two or three of them, (three or more if a bass channel is supported), all of them preamp level, meant to feed Surround sound self amplified desktop speakers. Never seen a receiver with a pin jack type LFE output. Only unamplified, or for some hybrid units, bass modules with multiple kinds of input taps are fitted with a pair of standard speaker (high level) level INPUT pinch connectors. Usually that kind would also have a second pair of two red, and two black pinch connector speaker OUTPUTS which would connect to the left and right speakers (the Mains) after the module stripped off the bass for itself This would also be a very old style way of doing things, or a made for stereo only bass enhancement module. Your "New Receiver" is likely some form of "inexpensive" Home theater in a box with completely non standard build, in which case there is no telling what kind of thing the odd plug is for, unless you are looking at the headphone jack and misidentifying it as a subwoofer LFE connector. look at the diagrams that came packaged (as they all do) with your unit. If you misspoke, and the LFE jack is the standard RCA jack, clearly marked LFE, it will likely not work with the high level inputs of you sub, as LFE signals are not amplified (low level) you would have to add another amp. In normal surround systems , it is expected that a self amplified subwoofer would be used. (has a wall chord on it) As noted, red and black pinch connectors are speaker level connections made to be driven , or to drive (depending whether they are inputs or outputs) by a fully powered amplifier, not a preamp signal. You can safely ignore the dyslexic thumbs down provided by some ignorant bystander. All the respondents here agree basically on what these taps, and their different types are for, and what they connect to.
You have a passive subwoofer. Which means it has no build in amplifier and requires power from the speaker level outputs of your receiver or amplifier to power it. So you would come off your main left and right outputs of your receiver or amplifier to the inputs of the subwoofer AND it should also have speaker level outputs to connect to your main speakers. So in theory your connecting the subwoofer 'inline" to the main speakers. The subwoofer will most likely also have a built in cross-over which will send only the bass frequencys to the subwoofer and everything else to your main speakers. Better subwoofers will have adjustments for both the cross-over points and a level control to adjust the output of the subwoofer to properly blend with the main speakers.
40 years high end audio video specialist
Hi so the system is incomplete as the amplifier which is needed to drive the sub is missing.