Can someone explain the right way to use SBT?

The way I use sbt is:

1. Use sbt-extras - just get the shell script and add it to the root of you project
2. Create a project folder with a MyProject.scala file for setting up sbt. I much prefer this over the build.sbt approach - it's scala and is more flexible
3. Create a project/plugins.sbt file and add the appropriate plugin for your IDE. Either sbt-eclipse, sbt-idea or ensime-sbt-cmd so that you can generate project files for eclipse, intellij or ensime.
4. Launch sbt in the root of your project and generate the project files for your IDE
5. Profit

I don't bother checking in the IDE project files since they are generated by sbt, but there may be reasons you want to do that.

You can see an example set up like this here.

Most importantly is probably, how do you find the right repositories and versions to include in your project? Do I just pull out a machette and start hacking my way forward? I quite often find projects that include everything and the kitchen sink

For Scala-based dependencies, I would go with what the authors recommend. For instance: http://code.google.com/p/scalaz/#SBT indicates to use:

libraryDependencies += "org.scalaz" %% "scalaz-core" % "6.0.4"

Or https://github.com/typesafehub/sbteclipse/ has instructions on where to add:

addSbtPlugin("com.typesafe.sbteclipse" % "sbteclipse-plugin" % "2.1.0-RC1")

For Java-based dependencies, I use http://mvnrepository.com/ to see what's out there, then click on the SBT tab. For instance http://mvnrepository.com/artifact/net.sf.opencsv/opencsv/2.3 indicates to use:

libraryDependencies += "net.sf.opencsv" % "opencsv" % "2.3"

Then pull out the machette and start hacking your way forward. If you are lucky you don't end up using jars that depends on some of the same jars but with incompatible versions. Given the Java ecosystem, you often end up including everything and the kitchen sink and it takes some effort to eliminate dependencies or ensure you are not missing required dependencies.

As a simple example, right now, I'm starting a brand new project. I want to use the latest features of SLICK and Scala and this will probably require the latest version of SBT. What is the sane point to get started, and why?

I think the sane point is to build immunity to sbt gradually.

Make sure you understand:

1. scopes format {<build-uri>}<project-id>/config:key(for task-key)
2. the 3 flavors of settings (SettingKey, TaskKey, InputKey) - read the section called "Task Keys" in http://www.scala-sbt.org/release/docs/Getting-Started/Basic-Def

Keep those 4 pages open at all times so that you can jump and look up various definitions and examples:

1. http://www.scala-sbt.org/release/docs/Getting-Started/Basic-Def
2. http://www.scala-sbt.org/release/docs/Detailed-Topics/index
3. http://harrah.github.com/xsbt/latest/sxr/Keys.scala.html
4. http://harrah.github.com/xsbt/latest/sxr/Defaults.scala.html

Make maximum use of show and inspect and the tab completion to get familiar with actual values of settings, their dependencies, definitions and related settings. I don't believe the relationships you'll discover using inspect are documented anywhere. If there is a better way I want to know about it.