Write project guide (#5195)

## Summary

Write the project guide that was added in
https://github.com/astral-sh/uv/pull/5135.

I tried to expand on details as much as I felt was necessary for someone
new to python package managers (which was myself a couple months ago).

docs/first-steps.md

@@ -23,7 +23,7 @@ These commands are intended for managing development of a Python project. In the
 - `uv sync`
 - `uv lock`
 
-See the documentation on [projects](./projects.md) for more details on getting started.
+See the [project guide](./guides/projects.md) for more details on getting started.
 
 ### Toolchain management
 

docs/guides/projects.md

@@ -1,32 +1,136 @@
 # Working on projects
 
+uv can manage the development of a Python project from the ground up.
+
 ## Creating a new project
 
+You can create a new Python project using the `uv init` command:
+
+```console
+$ uv init hello-world
+$ cd hello-world
 ```
-uv init
+
+Alternatively, you can initialize a project in the working directory:
+
+```console
+$ cd hello-world
+$ uv init
+```
+
+This will create the following directory structure:
+
+```
+.
+├── pyproject.toml
+├── README.md
+└── src
+    └── hello-world
+        └── __init__.py
 ```
 
 ### Working on an existing project
 
-<!-- What makes a project compatible with uv commands? What are my alternatives? -->
+If your project already contains a standard `pyproject.toml`, you can start
+using uv without any extra work. Commands like `uv add` and `uv run` will
+create the lockfile and virtual environment the first time they are run.
 
+If you are migrating from an alternative Python package manager, you may need to
+edit your `pyproject.toml` manually to use uv. uv uses the `[tool.uv]` section
+of the `pyproject.toml` to support non-standard features, such as development
+dependencies. Alternative Python package managers may use different sections,
+or a custom format altogether.
+
+## Project structure
+
+A project consists of a few important parts that work together and allow uv to
+manage your project. Along with the files created by `uv init`, uv will create a
+virtual environment and `uv.lock` file in the root of your project the first time you
+run a project command.
+
+### `pyproject.toml`
+
+The `pyproject.toml` contains metadata about your project:
+
+```toml
+[project]
+name = "hello-world"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+dependencies = []
+
+[tool.uv]
+dev-dependencies = []
+```
+
+This is where you specify dependencies, as well as details about the project
+such as it's description or license. You can edit this file manually, or use
+commands like `uv add` and `uv remove` to manage your project through the
+CLI.
+
+### `.venv`
+
+The `.venv` folder contains your project's virtual environment, a Python
+environment that is isolated from the rest of your system. This is where uv will
+install your project's dependencies.
+
+### `uv.lock`
+
+`uv.lock` is a cross-platform lockfile that contains exact information about your
+project's dependencies. Unlike the `pyproject.toml` which is used to specify the
+broad requirements of your project, the lockfile contains the exact resolved versions
+that are installed in the virtual environment. This file should be checked into version
+control, allowing for consistent and reproducible installations across machines.
+
+`uv.lock` is a human-readable TOML file but is managed by uv and should not be
+edited manually.
 
 ## Running commands
 
+`uv run` can be used to run arbitrary scripts or commands in your project
+environment. This ensures that the lockfile and virtual environment are
+up-to-date before executing a given command:
+
+```console
+$ uv run python my_script.py
+$ uv run flask run -p 3000
 ```
-uv run
+
+Alternatively, you can use `uv sync` to manually synchronize the lockfile and
+virtual environment before executing a command:
+
+```console
+$ uv sync
+$ python my_script.py
 ```
 
 ## Managing dependencies
 
-```
+You can add dependencies to your `pyproject.toml` with the `uv add` command.
-uv add
+This will also update the lockfile and virtual environment:
+
+```console
+$ uv add requests
 ```
 
+You can also specify version constraints or alternative sources:
+
+```console
+# Specify a version constraint
+$ uv add 'requests==2.31.0'
+
+# Add a git dependency
+$ uv add requests --git https://github.com/psf/requests
 ```
-uv remove
+
+To remove a package, you can use `uv remove`:
+
+```console
+$ uv remove requests
 ```
 
 ## Next steps
 
-See the [projects concept](../projects.md) documentation for more details on projects.
+See the [projects concept](../projects.md) documentation for more details about
+projects.