If you're a good musician or singer, make yourself very good, and look for ways to improve further. If you're excellent, make yourself brilliant and keep working at your craft. There's so much talented competition out there, and you have to be outstanding to get noticed, so whatever your ability level, continue to work on your musicianship and the presentation of your live show so that it becomes a seamless, well-polished production for your audience.
Don't undersell your material. Study the arrangements of your songs with a critical ear and edit them where needed so that they're focused and accessible. Songs that simply have potential won't be as attractive to a record label as songs that are well-crafted and have been structured to maximize their commercial appeal.
Even though the idea of getting signed is to record and release music, don't sit around and wait for a record deal before you release your own CD. If your budget is tight, simply record an EP of four or five songs and find a manufacturer who offers short-run orders. After you sell the first shipment, use the profits to order more. It is essential to gain valuable studio experience and end up with a CD you can use as marketing tool to increase your visibility and hopefully attract label attention.
One of the best ways to impress a record label is by demonstrating you are already a touring band with a loyal fan-base. Start by touring regionally, selling your CD at the shows and building a following one show at a time. After you've begun to develop a fan base, move further afield and tour on a national level. When you get to the point where you're able to attract an audience no matter where you play, you'll be so much more attractive to a record label because you're showing that you're already doing what will be expected of you if they sign you. The fact that you're already successful lessens the risk for them.
Don't sit and wait for labels to find you. Make sure you've got a professional press-kit complete with your CD, quality photos and a well-written bio ready to go. Make a list of the labels that are home to the artists you most closely identify with and send them brief, polite emails asking if you can send them your music and press-kit. If they say yes, send off your package in an envelope marked "Requested Material." Don't simply send out unsolicited mailings to every big label you can think of; this is expensive and ineffective. Targeting niche labels who have already signed artists in your genre will give you a far better chance of being heard.