The wonderful thing about researching a Soldier of the Canadian Expeditionary Force (CEF) is the accessibility of information available through the National Archives of Canada.
1. Attestation Papers: These contain the name, address, service number, next of kin, physical description and unit attested to. They can be searched by name or service number by using this LINK http://www.archives.ca/02/02010602_e.html
Although the attestation papers will give you the unit originally attested to (enlisted in) quite often soldiers were transferred to other units once they went overseas.
2. Service Records: These contain medical and pay records and give a more detailed and personal history of the soldier including what units he served with after going overseas. Full service records are not available online, but they can be ordered for a fee from the National Archives of Canada using this LINK
If the soldier you are you researching died during the war you can also check the Canadian Virtual War Memorial using this LINK
Further details can also be found on the Commonwealth War Graves Commission using this LINK
3. War Diaries: Once you receive the soldier's service records you can track their service overseas tracing where they were S.O.S "Struck Off Strength" or left a unit and where they were T.O.S. "Taken on Strength" or assigned to another unit, Once you have an outline of what units your soldier served in during particular times you can consult the unit war diaries of the Canadian Expeditionary Force available online using this LINK
The war diaries can be searched by unit and cover a specific block of time. By referencing the war diaries you can trace a soldier's service from rest billets to front line trenches. Unfortunately the diaries rarely mention anyone individually, except officers. The diaries normally list gallantry award recipients.
4. Further Reading: For a great overview of the CEF's role in the Great War, see Nicholson's Official History available as a PDF file using this LINK
David Love's "A Call To Arms" is an excellent organizational reference work and essential for any in-depth study of the CEF. It is available through the Naval & Military Press (ISBN 189425503-8).
There are also a number of memoirs and first person accounts available through CEF Books, these really give an impression of the ordeal of trench warfare and the toll it took on each individual. CEF Books are available online using this LINK
Another helpful source of information is the 1901 Census of Canada which is available and searchable online using this LINK.
Using the above online references, you can trace the service of your family member or the recipient of a medal you've discovered.