Fix install from source docs

In Qiskit#1439 we updated the install from source documentation to reflect
recent (as in the last year) changes to the build process and ensure the
documentation was correct for installing from source. However, in Qiskit#1507
where some of the documentation was refactored these changes were
inadvertadntly delete. This commit restores the correct source
installation instructions from Qiskit#1439 so that the hosted docs correctly
document how to build and install qiskit from source.

Fixes Qiskit#1624

docs/getting_started.rst

@@ -159,41 +159,17 @@ going to run and install the packages.  There are three main ways to do this:
 
           <h2>Installing Terra from Source</h2>
 
-       Installing from source requires that you have a C++ compiler on your system that supports
-       C++11.
+       Installing from source requires that you have the Rust compiler on your system.
+       To install the Rust compiler the recommended path is to use rustup, which is
+       a cross-platform Rust installer. To use rustup you can go to:
 
+       https://rustup.rs/
 
-       .. tab-set::
+       which will provide instructions for how to install rust on your platform.
+       Besides rustup there are
+       `other installation methods <https://forge.rust-lang.org/infra/other-installation-methods.html>`__ available too.
 
-          .. tab-item:: Compiler for Linux
-
-             On most Linux platforms, the necessary GCC compiler is already installed.
-
-          .. tab-item:: Compiler for macOS
-
-             If you use macOS, you can install the Clang compiler by installing XCode.
-             Check if you have XCode and Clang installed by opening a terminal window and entering the
-             following.
-
-             .. code:: text
-
-                clang --version
-
-             Install XCode and Clang by using the following command.
-
-             .. code:: text
-
-                xcode-select --install
-
-          .. tab-item:: Compiler for Windows
-
-             On Windows, it is easiest to install the Visual C++ compiler from the
-             `Build Tools for Visual Studio 2022 <https://visualstudio.microsoft.com/downloads/#build-tools-for-visual-studio-2022>`__.
-             You can instead install Visual Studio version 2015, 2017, or 2019 making sure to select the
-             options for installing the C++ compiler.
-
-
-       Once the compilers are installed, you are ready to install Qiskit Terra.
+       Once the Rust compiler is installed, you are ready to install Qiskit Terra.
 
        1. Clone the Terra repository.
 
@@ -207,19 +183,13 @@ going to run and install the packages.  There are three main ways to do this:
 
              cd qiskit-terra
 
-       3. Install the Python requirements libraries from your ``qiskit-terra`` directory.
-
-          .. code:: text
-
-             pip install cython
-
-       4. If you want to run tests or linting checks, install the developer requirements.
+       3. If you want to run tests or linting checks, install the developer requirements.
 
           .. code:: text
 
              pip install -r requirements-dev.txt
 
-       5. Install ``qiskit-terra``.
+       4. Install ``qiskit-terra``.
 
           .. code:: text
 
@@ -232,6 +202,24 @@ going to run and install the packages.  There are three main ways to do this:
 
           pip install -e .
 
+       Installing in editable mode will build the compiled extensions in debug mode
+       without optimizations. This will affect the runtime performance of the compiled
+       code. If you'd like to use editable mode and build the compiled code in release
+       with optimizations enabled you can run:
+
+       .. code:: sh
+
+           python setup.py build_rust --release --inplace
+
+       after you run pip and that will rebuild the binary in release mode.
+       If you are working on Rust code in Qiskit you will need to rebuild the extension
+       code every time you make a local change. ``pip install -e .`` will only build
+       the Rust extension when it's called, so any local changes you make to the Rust
+       code after running pip will not be reflected in the installed package unless
+       you rebuild the extension. You can leverage the above ``build_rust`` command to
+       do this (with or without ``--release`` based on whether you want to build in
+       debug mode or release mode).
+
        You can then run the code examples after installing Terra. You can
        run the example with the following command.
 
@@ -274,7 +262,7 @@ going to run and install the packages.  There are three main ways to do this:
 
           .. code:: text
 
-             pip install cmake scikit-build cython
+             pip install cmake scikit-build
 
        After this, the steps to install Aer depend on which operating system you are
        using. Since Aer is a compiled C++ program with a Python interface, there are