I'm going to assume (since you didn't specify) you want the next build to start only after the previous build has finished because there is some shared resource that they are using (e.g. for integration tests).
TeamCity has a setting to limit the number of simultaneously running builds, whether they are manually run or started by a trigger. Set the following option on the first page (General Settings) of your build configuration to "1":
Limit the number of simultaneously running builds (0 — unlimited)
Edit: TeamCity 8.0 announced today has added support for Shared Resources which allows you to define external resources and quotas for use across more than one build configuration.