I have been involved in drama for over 20 years and I have started three groups during that time. Once I took the lead on an established theatre and twice I started from scratch. I found a couple of good ways to start out.
One good way to start is with play readings. By doing play readings, this can be a good way to find people interested in acting or even find people interested in helping start the theatre group. Find a good public location like a public library with a meeting room, a church, a school or community center. I would discourage using your home because if want to do a public invitation to get new people and sometimes you get odd people showing up. You really don't want odd people knowing where you live :)
Play readings are also a great way to find plays that people might want to perform and also find out what kind of actors you have. Do the people who show up to the play reading prefer drama or comedy? Here is a great place to find free play scripts for your reading: http://www.freedrama.net
Another approach is to try theatre games (improv). Improv can be a fun way to see what types of actors you have in your community. Improv is also a great way for people to get to know each other and build a team. And you also find out who can work together and who is comfortable being on stage. Here are some great improv activities to get you started: http://www.freedrama.net/improv.html
Have play readings and/or improv nights more than once to see which people you have returning over and over. Then gather the people you feel can help you get a full production off the ground. Talk to this core group about what skills they have and what they would like to try. Find out who can sew and see if they want to try costumes. Find out who loves to go to garage sales and put them in charge of props. See who has good connections to businesses and have them handle fund raising and advertising.
Selling advertising space in your program for your first production can be a great way pay for your production before it even makes it on stage. I funded my first theatre group this way and when it came time to sell tickets, that was all profit because the advertising paid for all our expenses. But be sure to wait to sell ads until your rehearsals are off the group and it looks like you'll be ready to perform. You don't want to sell ads for a play production that doesn't make it to stage. And if you sell the ads within a month of your performance, it's a good way to advertise the show too. And be sure to give the people who advertise complimentary (comp) tickets - at least two for someone who does a quarter page ad. You can give additional rewards to bigger advertisers such as "meet the cast" for half a page ad or "come to the cast party" for a full page ad.
Be sure to keep careful records of all your funds. Sometimes it can be good to partner with a non-profit arts organization and have the funds be handled by them. Eventually you'll want to become your own non-profit so you can tap grant funding.
Overall, here are some good steps to follow:
1. Select the script
2. Read the script
3. Create a schedule (casting, practices, performance dates)
4. Find a location for practices and performing (might be two different locations depending on costs)
5. Casting call for actors
6. Select scenes for auditions
8. Cast actors
9. Meet with actors and read through script
10. Practice play (create a schedule that doesn't require all actors to be there all the time - work in a lot of time with the main actors)
11. Promote play performance(s) and keep promoting until the performance dates
12. Arrange for costumes, props, build set (I'd recommend you find people to do all these things for you if possible but check in on them as often as possible)
13. Dress rehearsals (have costumes, props, set, etc. and be in the performance location - invite friends, family and press/reporters for the final dress rehearsal)
14. Performances (invite more press/reporters if they all didn't make it to dress rehearsal; invite theatre reviewer if there is one in your town; give actors at least two free tickets for friends/family depending on how big your theatre venue is)
15. Opening night celebration after the performance
16. Closing night celebration after the performance (Cast Party)