My father is getting his citizenship through his grandfather who was born in the United Kingdom. As my dad was born in Canada, once he gets his citizenship, can I get my UK citizenship through him?
As your father was born outside the UK, once he gets his citizenship he will be a UK citizen by descent. UK citizens by descent generally cannot pass on citizenship to their children who are born outside the UK.
There is at least one exception however, in that if the UK citizen by descent lived in the UK for at least a 3 year period, they then can pass on citizenship. See http://www.wandsworth.gov.uk/info/200511/nationality_and_citizenship/1695/nationality_checking_service_ncs/5.
No. There are considerable limits to just how far back the acquistion of UK citizenship by ancestry will reach.
Edit: Your father qualifies to acquire UK citizenship through several possible scenarios because he had a grandparent who was born in the UK. However, unless you've described your lineage incorrectly, you do not have a grandfather who was born in the UK (it would be your great-grandfather). As such, there is no path to UK citizenship by this means according to current British nationality law.