You need the full handshake. Without it you have only the traffic after the handshake and not the keys.
To capture the handshake you have 2 options:
disconnect and reconnect a client from the network
force a deauthentication
To force a deauthentication you can use
aireplay-ng. The client will be disconnected, but will reconnect again automatically.
If you have Wireshark running before the authentication takes place, you will be able to decrypt traffic.
What kind of traffic? Unencrypted traffic only. You won't be able to read SSL data, for example. You can sniff clear text protocols: HTTP, Telnet, plain FTP. But not HTTPS, SIP, SSH, anything encrypted.