A decent soundboard recording depends on several factors.
To get the recording you are going to need a recording device and cables to connect to the board. You will generally find three types of outputs from soundboards: XLR, 1/4" TRS, and RCA. I carry one stereo RCA cable to 1/8" mini (that's what my recorder input is, YMMV) with XLR(M&F, just in case)>RCA and 1/4">RCA adapters.
Most important is the mix. Depending on the room, you may find that the output you are given is heavy on vocals and drums, two things that are mic'd and almost always come through the PA and not through amps on-stage. There are those rare exceptions where the sound guy mixes a separate output for tapers. I even had a sound guy tell me to come early the next time and bring headphones and I could mix my own feed. (I'm still surprised by this one.) I often have sound guys show me the slider or knob I can use for gain. Singer-songwriters are generally good for SBD recordings because there is often only vocals and a guitar, both coming through the PA. Listen in on the feed from time to time. I recently had one of the coolest sound guys on the planet show me where to plug in. I didn't check the feed. He came over at set break and apologized for giving me his monitor feed instead of the PA mix. Luckily i didn't need to use it because I was running two sets of mics as well in a great sounding room.
You also need a decent recorder that can take a hot signal or some kind of inline attenuator just in case. Not every sound guy is gonna let you adjust your levels on the board or even adjust it for you. Just remember they are there to do a job, and it's not making sure you get a smokin' recording. You'll want to use some headphones to monitor the sound for a bit. Sometimes these digital recorders can be deceiving. The levels may look good on the readout but you could be getting a distorted mess depending on how hot the signal is out of the board. The Sony PCM M10 is a popular choice around here. I have the PCM D50 and I love it. The smaller, inexpensive Tascams DR-0x work well if you are on a budget and know what you are doing, but they will overload at a much lower level than the other recorders out there and will probably need some type of attenuation at some point. M-audio makes an inline attenuator for $20, but that adds another link in the chain and closes the price gap with the M10 a bit.
If you are going to be taping in the same venue a lot, get to know the sound guy. Find out his favorite drink or whatever and get him one from time to time, even if he gets it free from the venue. Compliment him on the mix and always say thank you for the patch. The most important thing is to stay out of his way if he's busy. If the band starts and I'm not getting a signal, I usually don't speak up until set break. Or I wait until the sound is dialed in and try to let him know with hand signals. I have seen tapers frantically waving at the sound guy the second the first note hits and they are getting nothing. I have even seen people enter the soundboard cage or go crawling all over the back of the board, plugging and unplugging. Don't be that guy.
All that said, I only get board feeds in venues where the sound is crappy or the audiences are particularly loud. And then I often don't mix it in at all if the audience or stage lip recording sounds good.