Welcome to Rootschat.
The first thing you need to do is register - for free on
www.scotlandspeople.gov.uk - (referred to here as SP). There is a lot of free information relating to Scottish research there. It's the govt pay per view site. £6.00 buys 30 credits which allow for the search and download of 5 certs - assuming a first time hit.
I've just been on the site and for 1 credit found that between 1870 and 1900 there were 3 Andrew Grahams born in Hawick.
1890 GRAHAM ANDREW ANGUS M HAWICK /ROXBURGH 789/00 0149
1887 GRAHAM ANDREW BEATTIE M HAWICK /ROXBURGH 789/00 0148
1880 GRAHAM ANDREW ELLIOT M HAWICK /ROXBURGH 789/00 0022
Scottish certs after 1855 give both parents names and occupations and maiden name of mother.
Scottish census records start in 1841 and currently you can view them online on SP up till 1901.
Can you be really clear when you post e.g - I take it that Andrew Graham is your maternal grandfather? Or was the name you were looking for Andrew Graham Bell?
SP will give a table of what's downloadable online. Feel free to ask for help - you'll get it :O)
Once you get back into the 19th century,
www.familysearch.org (free) is a useful tool.
Regards, Steve .....