Hi Speedy
...and welcome to Talking Scot
First thing to do would be to go to Scotlands People and search for the birth of Mary, as you have a date for her.
There is a record there for a
Mary Buchanan Shennan b. 1896 Lanark, so you will find her easily.
Where did you find the date?
Her birth entry will give her parents names. You could then search for Mary & Duncan's marriage (again,
it is easy to find - in 1921) - this will give you the names of Duncan's parents and his age. A good next move would be to try to find them both in the 1901 census, because Duncna and Mary will be small children and should be living with their families so that helps you a great deal. The census is also available on Scotlands People (original images), or transcriptions of the 1901 on Ancestry (you may be able to get free access to this at your local library). From there you can search for Duncan's birth as you will then know where he was born. You will need to know this as there will be too many Duncan Robertsons otherwise!
Also, you can go back in time by searching for the marriages of the two sets of parents given in Mary & Duncan's marriage, and using the census data to find out more about the family.
www.scotlandspeople.gov.uk
www.ancestry.co.uk
Best wishes
Lesley