How do we make studying Torah by adults a central part of our synagogue?
Your first goal should probably be some popularly-attended classes, which you can expand out from.
Start with one class. Here are some tips for making it popular, based on my experience in youth programming, scheduling things at Hillel in college, and participating for a few years now in a weekly Talmud seminar.
Schedule it at an optimal time. Sunday morning with breakfast, as N123 suggested, works well, as can some dinner times if you serve dinner and are targeting a demographic that doesn't include too many parents of young children. In general, pick a time when people in your target demographic are less likely to be busy. If there are many young parents, don't schedule during their kids' bedtime. If there are many football fans, don't schedule for Monday night. Etc.
If there's a particularly well-attended prayer service, consider scheduling immediately before or after. This could work particularly well for a ~10-minute mini-class, which people will feel like they might as well stay for as long as they're there already.
Pick a topic people are interested in and a good presenter who's good at involving the audience while maintaining control of the class.
Don't just advertise the class and expect lots of people to come. First, approach a bunch of people who you think might be interested and invite them personally to attend. Then, ask them to invite their friends. (Kind of like what we're doing here with mi.yodeya!)
Do advertise. Do whatever you can when the class is starting out to get its existence into everyone in the congregation's consciousness. Have the Rabbi promote it during his sermon. Etc. Repeat this sort of blitz something like annually.
Consider making the opening of the class into a special event, maybe with a special guest speaker and food.
As the class continues, have the speaker determine a title for each session ahead of time, then put this title into the class's place in the congregation's weekly announcements (email, written, and verbal). If you really want to be aggressive, especially in the frist few weeks, make a new flyer for each session featuring its title and post them around the synagogue ahead of time. Changing material is harder for people to ignore than a static announcement.
Once you have one class thriving, expand out into additional classes. Consider having at least one class that requires preparation of a text ahead of time, then schedule time before the class (or elsewhen in the week) when there is a study room open for people who want to do their preparation there, staffed with someone who can answer questions. Also, offer to match people up to study together. If you can create a situation in which people are meeting their friends to study, you're well on your way to having Torah study be central to your synagogue.
I don't know what level the people in your synagogue are holding at. If they are holding at a decent level, try making a night beis medrash program for an hour a night. One night have chavrusa (one on one) learning. One night have a shuir (lecture) in halacha. One night have a shuir in gemara (talmud). One night in mussar (ethics). Etc.
If they are beginners, try having a one night a week shuir on simple chumash (bible).
Sunday morning shiurim (clases) usually get great results if you have breakfast with it. People aren't working so they are willing to come.
In addition to this excellent advice, make it easy for people who've heard about it to join in the middle. Divide a year-long class into shorter segments, maybe 4-6 weeks each, to provide some good entry points. For example, we ran a beginner class on the prayer service and made it clear that if you missed the classes on kri'at sh'ma you could still come to the ones on the t'filah and you wouldn't "be behind".
Also, celebrate milestones. We have a long-running torah-study class (not parshat hashavua but "start at the beginning and it takes as long as it takes"), and at the end of each sefer we make a big party. At the end of the first cycle we had an even bigger party, with members of the class giving short divrei torah and lots of Q&A and discussion. We invited everybody to this, not just the students, and got some new learners to start the next cycle.