This particular phrase comes from《诗经·秦风·无衣》
Full: 岂曰无衣？与子同袍。王于兴师，修我戈矛。与子同仇！
Translation:
Who said that you have no clothes to wear,
I will share with you my robe.
The king has called upon us that,
we make ready with spears and Ge's (戈)，
we fight against our enemies.
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"于" serves as an auxiliary verb here. Its exact meaning has lost AFAIK. My guess is that it indicates a present continuous tense, as in "黄鸟于飞 (a yellow bird is flying)" （also from 《诗经》）。So maybe a better translation is "... The king is calling upon us that ...". – John Z. Li Apr 15 '19 at 1:51
子是对男性的敬称，here it means "you".
In your quote 与子同仇，it means
（我）与你同仇敌忾
Similarly, we call 孔仲尼 as 孔子 to show respect. Also we have 庄子、墨子、孟子、老子……
