Go to:
1. City Overview
2. Click on your academy ( behind the senate and to the right of barracks)
3. You should see an overview of all the things you can research. Find archers. (They are on the first row on the left hands side, second picture down).
4. You need the following to research archers but:
-550 wood
-100 rock
-400 silver
-8 research points.
5. If you have all that, just click the photo of the archer and it should start researching.
+ Rep if this helped you :')
-CheezeHead.