The four string bass in standard tuning starting with the thickest string is: E ~ A ~ D ~ G. This tuning will be the starting point for beginners, although some professional bassists rarely stray this time tested tuning.
Start with a fresh set of strings. Many bassists prefer GHS Boomers as they work for fingered or picked playing, but you will need to do a bit of research depending on the genre or style. There are even fretless basses, which have a distinct sound when sliding up and down the fretboard.
Follow the instructions above and really try to listen. Each note is perfectly tuned to 440 Hz, so all you have to do is let the sound sink in. When playing the corresponding bass guitar string, you can twist the tuning peg to really try to get as close as possible. Eventually, you'll be able to tell that you are indeed, in tune.
Do this for each string and do your best to really be precise. Afterward, try and test your results on a digital tuner. Do this every single time you tune the bass guitar and your playing will improve.
Why not just take the easy road and tune with a digital tuner in the first place? Because it encourages tuning 'by sight' which does not require listening. Sure, it's helpful in a loud bar, but if you really want to giant leaps of improvement, you must improve your hearing and pitch recognition. This can only lead to improved playing and heightened sense of pitchGoogle+