There is not a lot to learn to understand the basics, but maybe one step that's not necessarily documented is the overall workflow and why it's arranged this way. You mentioned the LLM "using web search" and it's a related idea: LLMs don't run web searches themselves when you're using an MCP client, they
ask the client to do it.
You can think of an MCP server as a process exposing some tools. It runs on your machine communicating via stdin/stdout, or on a server over HTTP. It exposes a list of tools, each tool has a name and named+typed parameters, just like a list of functions in a program. When you "add" an MCP server to Claude Code or any other client, you simply tell this client app on your machine about this list of tools and it will include this list in its requests to the LLM alongside your prompt.
When the LLM receives your prompt and decides that one of the tools listed alongside would be helpful to answer you, it doesn't return a regular response to your client but a "tool call" message saying: "call with ". Your client does this, and sends back the tool call result to the LLM, which will take this into account to respond to your prompt.
That's pretty much all there is to it: LLMs can't connect to your email or your GitHub account or anything else; your local apps can. MCP is just a way for LLMs to ask clients to call tools and provide the response.
1. You: {message: "hey Claude, how many PRs are open on my GitHub repo foo/bar?", tools: [... github__pr_list(org:string, repo:string) -> [PullRequest], ...] }
2. Anthropic API: {tool_use: {id: 123, name: github__pr_list, input:{org: foo, repo: bar}}}
3. You: {tool_result: {id: 123, content: [list of PRs in JSON]} }
4. Anthropic API: {message: "I see 3 PRs in your repo foo/bar"}
that's it.
If you want to go deeper the MCP website[1] is relatively accessible, although you definitely don't need to know all the details of the protocol to use MCP. If all you need is to use MCP servers and not blow up your context with a massive list of tools that are included with each prompt, I don't think you need to know much more than what I described above.
[1] https://modelcontextprotocol.io/docs/learn/architecture