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See [[Using Git|Using Git]].
There are several different branches of V8; if you're unsure of which version to get, you most likely want the up-to-date stable version. Have a look at our [[Release Process|Release Process]] for more information about the different branches used.
You may want to follow the V8 version that Chrome is shipping on its stable (or beta) channels, see http://omahaproxy.appspot.com.
V8 public API (basically the files under include/ directory) may change over time. New types/methods may be added without breaking existing functionality. When we decide that want to drop some existing class/methods, we first mark it with V8_DEPRECATED macro which will cause compile time warnings when the deprecated methods are called by the embedder. We keep deprecated method for one branch and then remove it. E.g. if v8::CpuProfiler::FindCpuProfile was plain non deprecated in 3.17 branch, marked as V8_DEPRECATED in 3.18, it may well be removed in 3.19 branch.
We also maintain a document mentioning important API changes for each version.