The official answer is that you go to 
www.scotlandspeople.gov.uk, invest in a few credits and use 6 of them to find, view and download an image of the certificate on the spot. It works out at £1.50 per certificate. 
However seeing you're new to SP I took a look. James Clark's parents were Robert Clark and Ann Philip, and Elizabeth Simpson's were James Simpson and Elizabeth McGlashan.
Further investigation of the indexes at SP reveals that Robert Clark and Ann Philip were married in Monifieth in 1840. Their son James was baptised in St Vigeans in 1844, one of six recorded children. 
In the 1851 census the family was in Ponderlaw Street, St Vigeans, which is actually in the burgh of Arbroath: Robert, 39, labourer at gas work, born Crathie, Aberdeenshire; Ann, 31, born Strathmartine; daughter Ann Alexander, 14, born Monifieth; James, 7; Margaret, 4; and Robert, 2, all born St Vigeans.
In 1861 they're in South Leith: Robert, 50; Anne, 41; James, 17; Margaret, 14; Robert, 12; William, 9; Betsey, 7; Peter, 4 and Isabella, 1. 
By 1871 Ann was widowed and had moved to England and was living in West Ham with some of her children. This explains why I can't find Ann's death certificate in Scotland. Scottish death certificates tell you the names of the parents of the deceased, inclding their mother's maiden surname, but unfortunately English (and Welsh, and Irish) ones don't.