I'm going to hijack a post from Tim Challies' blog because it is so helpful. He offers some great suggestions (picked up from a Nine Marks article) on how church members can serve their church on Sunday morning.
He recommends that before the morning worship service you read over the sermon text, pray for the gathering of the congregation, think strategically about who to sit with (note: this is not disingenuous; it is thoughtful), arrive early, and greet newcomers.
During the service he recommends you "sing with gusto" (we are singing unto the King Eternal), help with logistics- or as I prefer- jump in and help "put on fires", guard your mind against distractions, listen carefully, and be conscious of your body language (those sitting near you will pick up on frowns or fading eye-lids).
Then he recommends some things for after the service... connect with newcomers (go to them and don't wait for guest to approach you), exchange contact information with them, start a conversation about the sermon ("what did you think about such and such statement?" or "that was something I've really been chewing on, how about you?"), ask someone (even a member you've known for some time) how they became a Christian, and don't rush out-- you might be rushing past opportunities the Lord has prepared for you to fellowship or minister.