First you need to get around 100 like minded people who think the same as you and who are registered to vote in the constituency (about 10 people registered in a ward should be enough to remove a councillor).
Meet somewhere discreet, keep it to yourselves as much as possible, decide who will be your candidate. Then you need to all join the Labour party, but stagger it over a period of a few months - so it would be more difficult for the party to get wind of what is happening - because if your candidate wins, they will try to invoke any rule they can to stop you or appeal to the leadership to make one up to stop you.
They will call any attempt to outvote them 'entryism' - actually it is called 'democracy', but leftwingers are not supposed to have democracy within the Labour party. The throwing out of 'lefties' in the Eighties has inevitably led to stalinist Brown and the collapse of the party, but don't expect the right-wing clowns who currently run the party to see it like that. Rather than try to get more members to outvote those who had joined (which is the democratic approach), they decided to chuck out all the people they didn't like - mainly lefties and then fix right-wing policies they liked instead. Democracy no chance!
Each constituency has different rules on how long you have to be a member before you get voting rights but it is usually no more than 12 months membership and sometimes 6 or less.
Only a few of you need to attend ward and constituency meetings - get a few of you on the GC (general committee) and LGC (local government committee) if you can. It shouldn't be too hard.
Active members are very short on the ground in most constituencies and although they won't initially welcome you, if you avoid being radical they won't suspect you. Once you have gone through the motions for a few months and delivered a few leaflets and canvassed a bit, you might be grudgingly accepted. But watch out for the secretary of the party they are usually the right-wing lynchpin and two-faced bastards.
All you have to do now is trigger a de-selection and get your candidate through the ward selection process - you will need at least 10 active members on one of the wards. Once they get through to the final selection meeting, you can either turn-up in force or better still fill out a postal ballot. Then wait for all hell to break loose and keep your heads down.
If anyone can tell me of any mistakes I have made here or extra information please let me know and I will correct and update. Good luck.
By the way, I imagine you could follow this approach with a Lib Dem MP, but not the Tories - they have no internal democracy at all - all their candidates are decided by their leadership!