How can I programmatically build a Visual Studio solution?

You're going to have to launch a process at some point to do the compilation, so you might as well spawn a process to kick off the compilation. It is going to be much easier than struggling with an API.

Andrew gives some good advice about how you might go about it, but I still think it is a mistake.

As itowlson pointed out, you could also use the Build Engine APIs.

... from MSDN ...

// Build a project file
bool success = engine.BuildProjectFile(@"c:\temp\validate.proj");

You can use MSBuild from a script such as a batch file. And just check the ErrorLevel for something other than 0... or you can have fun with the APIs.

C:\Windows\Microsoft.NET\Framework\v2.0.50727\MSBuild.exe

.. from msbuild.exe /? ...

Microsoft (R) Build Engine Version
2.0.50727.4927 [Microsoft .NET Framework, Version 2.0.50727.4927]
Copyright (C) Microsoft Corporation
2005. All rights reserved.

Syntax: MSBuild.exe
[options] [project file]

...

Examples:

    MSBuild MyApp.sln /t:Rebuild /p:Configuration=Release
    MSBuild MyApp.csproj /t:Clean /p:Configuration=Debug