best analysis software for league games

Hi I was just wondering what people think is the best software for analysis games for mistakes?

Does chess.com have this sort of facilitie or do i need to purchase one?

It does. Go to the game you want reviewing from your archive and choose computer analysis. Within an hour or two you'll get a message from chess.com letting you know that your analysis is ready.

is it free and can i enter games i played in real life?

No I don't think so, just games played on chess.com.

Basic members get one free analysis a week

so the only way to get my league games analysed would be to play them out online with someone here and then ?

There are many free software options for computer analysis of chess games. I would personally start with SCID (scid.sf.net).  It comes with a couple of free chess engines pre-installed, but you could install the best free one, Houdini 1.5 or Stockfish if you'd rather.

is there any way to analyse my games online?