ZNC is already running (install). Client connects to the bouncer, not straight to the IRC network.
Server line
Host: bnc.kire.net (A 70.39.109.170) or the vhost you bound. Port: whatever you picked in --makeconf. TLS if you enabled SSL.
/server bnc.kire.net PORT
Password is username:password. If you have multiple networks in ZNC:
username/network:password
Some clients have separate "server password" vs SASL — this is the server password to ZNC. Ident: your shell username unless you set otherwise in the ZNC user.
Playback
If you loaded the playback module (/msg *status loadmod playback or makeconf), clients that speak it will request only what they missed instead of the whole buffer. irssi/weechat: use a playback/znc script or cap. Everyone else gets the classic buffer dump on connect. Keep buffer sizes sane.
Run irssi/weechat in screen/tmux on the shell if you want; that is what screen is for. ZNC itself stays a daemon.
Vhost / ident
Set BindHost (vhost) on the ZNC user or network in webadmin. Ident is the ZNC user ident field. Changing either: edit znc.conf or webadmin, then reconnect the client.
/msg *status help
/msg *status listavailmods
Forgot the password: reset. Bouncer will not stay up: restart.
AUP: max 2 IRC connections per shell to a given network — the bouncer's uplink is one of them.