Where's the line between friends and lovers?

When you jump in the shower with someone, that's a good indication that a line has being crossed. Receiving the paramour achievement is another good indicator.

The game has lock-in moments for all the romances. These are points of no returns for choosing your soul-mate. Some examples include:

1. Speaking with Liara on the Presidium near the markets after Priority Citadel II
2. Speaking with Ashley/Kaiden at the Appolo Cafe.
3. Calling Tali up to your quarters for a private discussion.
4. Having Traynor up to your cabin for game night.
5. After one of the interviews with Diana* (This may not lock you in, because she does not count as a normal Paramour Achievement granting romance option.)
6. The shooting match with Garrus.
7. Dancing with Cortez in Purgatory.
8. Meeting with Miranda in a room off the Presidium Commons after Horizon.
9. Meeting with Jack at Purgatory after Grissom Academy.

You have to pick dialog options in each of these instances to confirm the romance. These instances will invalidate any other possible romance. You can tell anyone you have feelings for them, before this point, and it shouldn't exclude any other options.

The details are in CaulynDarr's answer, but the really short answer to the general question is that in each case there is a clear dialogue choice that indicates whether you wish to pursue romance or not.

For example, with Allers, she clearly flirts with you by saying something like "If you keep feeding me like this I might follow you home" and your possible answers are "I'm meat" (or similar) or "Let's keep this professional".

It's not really possible to stumble into a romance unexpectedly.