I'm having trouble getting clang++ to work as I compile my code. Specifically, I'm getting a make: clang++: Command not found error.

I've run sudo apt-get install llvm, and also sudo apt-get install build-essential and sudo apt-get update. What do I have to do to get clang++ installed?

Installing the llvm and build-essential packages, as you have done, does not cause clang or clang++ to be installed. For that, you must install one of the clang packages, depending on which version of clang and clang++ you want.

16.04

In Ubuntu 16.04, your options are clang-3.5, clang-3.6, clang-3.7, and clang-3.8.

14.04

In Ubuntu 14.04, your options are clang-3.3 , clang-3.4 , and clang-3.5 .

You can install them in the Software Center, or with:

sudo apt-get update
sudo apt-get install clang-3.n

(Replacing n with the desired sub-version, of course.)

12.04

If you're running Ubuntu 12.04, there's only one package that provides clang and clang++, so it's just called clang .

18.04 (Bionic)

I visited http://apt.llvm.org/bionic/dists/ (i.e. bionic distributions).

I determined that 6.0 was the latest major version of the toolchain.

I assume that you'll want the linker, lld, also.

# grab the key that LLVM use to GPG-sign binary distributions
wget -O - https://apt.llvm.org/llvm-snapshot.gpg.key | sudo apt-key add -
sudo apt-get update
sudo apt-add-repository "deb http://apt.llvm.org/bionic/ llvm-toolchain-bionic-6.0 main"
sudo apt-get install -y clang-6.0 lld-6.0

This gives you binaries with the following names (and more, probably):

clang-6.0
clang++-6.0
lld-6.0
ld.lld-6.0

It also installs these packages (and more):

llvm-6.0
llvm-6.0-dev
llvm-6.0-runtime

17.04 (Artful)

Same as above. I'll repeat every line for convenient copy-paste.

# grab the key that LLVM use to GPG-sign binary distributions
wget -O - https://apt.llvm.org/llvm-snapshot.gpg.key | sudo apt-key add -
sudo apt-get update
sudo apt-add-repository "deb http://apt.llvm.org/artful/ llvm-toolchain-artful-6.0 main"
sudo apt-get install -y clang-6.0 lld-6.0

16.04 (Xenial)

The accepted answer already gives instructions for installing clang-3.8 on 16.04, but here's how to get clang-6.0:

# grab the key that LLVM use to GPG-sign binary distributions
wget -O - https://apt.llvm.org/llvm-snapshot.gpg.key | sudo apt-key add -
sudo apt-get update
sudo apt-add-repository "deb http://apt.llvm.org/xenial/ llvm-toolchain-xenial-6.0 main"
sudo apt-get install -y clang-6.0 lld-6.0

Installing Clang 9 on Ubuntu 18

sudo apt-get install clang-tools-9

It will also install llvm-9

For more information follow clang documentation.