In the best of cases, to determine whether a DNA segment is a match with a cousin on the maternal or paternal side of the family, it is helpful to also have your mother and father also submit a sample. However, both of my parents passed away several years ago so it is a little more difficult.
Fortunately, one of my first discoveries on 23andMe were two closely related cousins. One was the great granddaughter of my maternal aunt (1st cousin, twice removed) and the second was the granddaughter of my maternal grandfather's sister (2nd cousin). Plus, a 3rd cousin on my father's side of the family had already done much analysis on my paternal great grandmother's family. Those matches have been invaluable in distinguishing the maternal vs. paternal.
For example, on chromosome 5, there are six cousins on the same segment. I didn't display all the relationships between each cousin but in the first set, everyone matches each other. Since I know both Leah and Shirley are cousins on my maternal side, I know that I am related to B J on the maternal side and perhaps farther back than my great grandparents because the segment length is much smaller.
Set 1 - Maternal side match
Rebecca vs. B J 5 162000000 167000000 7.0 cM 1030
Rebecca vs. Leah 5 163000000 172000000 17.9 cM 2420 (Maternal grandparents in common)
Harry vs. Shirley 5 167000000 180000000 28.4 cM 3035 (Maternal great grandparents in common)
Since the cousins in set 2 also all match each other but none of my cousins in set 1, we can conclude that we are related ton my paternal side.
Set 2- Paternal side match
Rebecca vs. Christopher 5 171000000 175000000 11.4 cM 1160
Rebecca vs. Walter 5 171000000 177000000 14.4 cM 1418
Rebecca vs. Willis 5 171000000 177000000 14.3 cM 1406
While I don't have the common ancestor for everyone here yet, I am able to eliminate half of my family tree and I can tell anyone matching on this segment where to look.
I find that associating that one little bit of DNA to one of my remote ancestors exciting. Early on I was contacted by another cousin and found that we were related to each other on a small segment through my 4th great grandfather. How cool is that!
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