If you hold a machine-readable UK passport and you've never been arrested or convicted of an offence, you're eligible to enter the USA under the Visa Waiver Program. (There are certain other exceptions, including people who've previously been refused entry into the USA, but I'm assuming these don't apply to you).
This VWP applies even if you enter the USA from Canada. (You must be in possession of a travel ticket for leaving the USA and you have to complete a form and pay a $6 fee):
http://www.usembassy.org.uk/cons_new/visa/niv/ vwp.html
If you don't qualify for entry under the VWP, you'll have yo apply for a visa. For anyone who's ever been arrested or convicted of an offence, the process takes at least 5 months so, obviously, you would need to apply well before travelling to Canada. (Note that, for much of that 5 month period, you're passport will be held by the US authorities so you won't be able to travel to Canada or anywhere else, apart from Ireland, outside of the UK ).
The process for applying for a visa is explained in my posts here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
(In order to get the links to work, you should read the last post before the others).
Chris