Every child is different in temperament and expectations/needs and the first child usually is a 'good' baby and lulls you into believing 'Hey, This parenting thing is EASY!', Then child #2 disperses ALL your preconceived notions about parenting! LOL.
At age one, kids are able to DO lots of things but aren't able to SAY a lot, express their feelings, etc. Have you checked out baby sign language? It might help to a degree.
Kids usually only 'act out' when they're hungry, thirsty (which is easy to forget when they quit nursing breast or bottle), tired, cold/hot, frustrated, sick/uncomfortable, etc so try to think over that mental list in each scenario. If none of that works, ignore the behavior as much as possible (without ignoring the CHILD). The less attention they get from you about it (I mean you trying to 'solve' the problem), the worse it can get, though. Sometimes they just need put to bed (in a crib, alone in a quiet room). Sometimes they need cuddling and soothing talk.
Read anything about parenting by Kevin Lehman. He's wonderful!