^^ what he said. Tabs will give you the notes / frets to play but not the rhythm so make sure you're learning a song that you know. I know, bit of a silly thing to say, but it happens.
Another really crucial part to playing is technique. It may seem boring and pointless but in the end all it does it help you become a better player in less time. So...
Sitting down and playing: Most players will put the bass / guitar on the right knee and play from there. I feel the best way to play whilst sitting down is to use the classical guitar technique of putting the bass between your legs where the neck of the bass is on a sort of 45 degree angle. That way your wrist on your fretting hand is not bending at right angles to reach the strings, which would end up cutting off the transfer of energy from your forearm tendons to your fingers, so that's one reason to play the bass sitting between your legs.
Another reason for having your bass between your legs is that it imitates the position the bass would be in when playing standing up with a strap, so when you decide to stand up and play it will feel natural.
Here's a picture for reference:
Right hand: You want to be relaxed! Light as a feather! If you find that your right hand isn't strong enough to play as loud as you would like then just turn your amp up! You will find the more you play the more strength will come to your fingers, regardless of how soft or hard you play. So just chill.
Two fingers are better than one! Practise alternating your index and middle fingers on all the strings. So 4 plucks on the E string, the lowest sounding one, (middle, index middle, index) 4 plucks on the next string and so on, then go back down. If you want you can mix it up by reversing the order (index, middle, index, middle) Remember, relax!
Left hand: The same principle to the right hand, you want to be relaxed. If you try it out, you'll find that it really doesn't take that much pressure to push down the string to play a note. So just be aware of that when you play.
A really good exercise for building left hand strength and dexterity is what is called a chromatic exercise. Basically you want to play, whilst using the alternating fingers of index, middle like in the last exercise, the first 4 notes of each string, one after another. So, frets 1, 2, 3 and 4 on the thickest string, then move up to the next one and play the same. The trick is, like many beginner bassists find, like me, that you may want to avoid using your pinky finger. Well, you gotta use it. For fret 1 use your index finger, fret 2 use your middle, fret 3 use your ring and fret 4 use your pinky, so that your fingers move in the same sequence as the frets. Your hand should be looking something like this (don't worry about what frets he's on) -
Also, if you want to do a variation of the exercise play the notes in reverse order, so frets 4, 3, 2 and 1 in that order. I know, it doesn't sound very musical at all but it is going to help you trust me. Also, don't focus on playing this as fast as you can, play it as slow as you have to to get through it. Playing this exercise a few times is bound to make your hand ache but all that means is that you're progressing and you're fingers are getting stronger. Isn't that wonderful?
In the way of beginner pieces to start learning all I can think of is Seven Nation Army by The White Stripes
The song
YouTube - The White Stripes
The tab -
Seven Nation Army Bass Tab by White Stripes @ Ultimate-Guitar.Com
Maybe someone else can recommend some good beginner tunes?