There are two options at least:

A) If exposed as HTTP, the simplest way is to create an endpoint on your container like:

GET /ping

or

GET /health

You could also use the index route:

GET /

In the Kubernetes config:

readinessProbe:
  failureThreshold: 3
  httpGet:
    path: /ping {YOUR PATH HERE}
    port: 8080  {YOUR PORT HERE}
    scheme: HTTP
  initialDelaySeconds: 5
  periodSeconds: 10
  successThreshold: 1
  timeoutSeconds: 1

And have it return a 200 status.

Without knowing your language of choice, here is one in Node.js with Express:

var express = require('express');
var router = express.Router(); 
router.get('/ping', (req, res) => { 
    res.json({
      env: process.env.NODE_ENV
    });
});

Here would be one using Rust and Actix:

async fn ping(_req: HttpRequest) -> impl Responder {
    format!(
        "I am healthy: {} v{}",
        env!("CARGO_PKG_DESCRIPTION"),
        env!("CARGO_PKG_VERSION")
    )
}

B) If not using HTTP, then one way is to have your process write to a file every minute to confirm healthiness

Here is an example for the Kubernetes config:

readinessProbe:
  exec:
    command:
      - test
      - '`find .health_check -mmin -1`'
  initialDelaySeconds: 5
  periodSeconds: 15

I can expand on this more in another article if desired!