Strike Forces (SF) are the common way to capture foreign cities ( read: enemy cities). These are used in both KnC and TLK.
SFs are usually composed by onliners, who join an army together ( visit castle, click join on the SF army). The SF leader, who is the highest rank in the SF, and has created the army, will then go to the border and attack the city your country wants to capture.
How to join an SF:
1) Go to the city where the SF is ( if you were in the Main Army, you usually will already be there).
2) Click city centre.
3) Click visit castle
4) Join the appropriate army by clicking join.
5) When the SF leader strikes, you will receive a message: "You participated in a battle, you can see the results in the battle log."
6) Usually you will need to join a taxi or move back to the main army.