Quick And Dirty Guide To Apostrophes

The laws of electrodynamics state possible values of the angular momentum vector, in the non-inertial body frame, for a free, asymmetric top is a surface of constant energy, and the closed curves are given by the intersection of that ellipsoid with spheres of various radii, corresponding to different values of the total magnitude of the angular momentum.
As it is a law, and as i have no idea what any of any of the above means, it is possible that i have at some point broken that law and could possibly be breaking it now so will hand myself over to the correct authorities as soon as i have finished this post.
Something else that has rules which MUST BE OBEYED is the English language but according to linguists, the English language is one of the hardest to learn and there are no shortage of grammar Nazi's who will try to pick you up if you use the word 'less' instead of 'fewer' or you misspell manouvre manouvere manoeuvre.
It is due to the British Empire and the spreading of it's tentacles back in the day that English is the most practised second language and then along came the World Wide Web with the majority of pages written in English although this percentage has dropped in recent years.
Probably the most common area students go wrong is the use of apostrophes which can either go in words, after words or go missing altogether but another problem area is to/too and a/an.
A quick, dirty guide to apostrophes is if you are shortening two words into one word (there is, was not) then you use an apostrophe to show what you have done so 'there is' becomes there's and 'was not' become wasn't.
It is also used to show possession of something so as this blog belongs to Lucy, it would be Lucy's Blog or a cake that belonged to Paul would be Paul's cake.
The hardest apostrophe to understand is the one that goes after a word which ends in the letter 's' when there are more than one of something. For example you can go to a boys' school (more than one boy), go on holidays in three days' time (more than one day) or go to a festival to watch bands' play (more than one band).
If something is not plural ending in s or doesn't belong to anyone, you can discard the apostrophe altogether so it's a sports car or sport photos as the sports doesn't possess the car or photos. 
The To/Too rule of thumb is if you can replace the to/too with the word 'also', then it should be 'too', if the word after the to/too is a place then it's 'to'. For example you go TO the shops' to buy clothes and go TO the airport to catch a plane but once at the shops' you can buy a latte TOO or at the airport you can buy a newspaper TOO.
A/An is easy to remember, if the following word starts with a vowel it's AN, if not it's A so you have a spark plug but an engine or an eagle but a parrot.      
There are variations on these themes and a grammar Nazi will point out when these rules are not applicable but as a rule of thumb, these will get you through but remember that the most important thing is not how you say something but what you are saying.