Add a reference to the Elastic.CommonSchema.Serilog package:

<PackageReference Include="Elastic.CommonSchema.Serilog" Version="8.6.0" />

var logger = new LoggerConfiguration()
    .WriteTo.Console(new EcsTextFormatter())
    .CreateLogger();

In the code snippet above new EcsTextFormatter() enables the text formatter and instructs Serilog to format the event as JSON. The sample above uses the Console sink, but you are free to use any sink of your choice, perhaps consider using a filesystem sink and Elastic Filebeat for durable and reliable ingestion.

In ASP.NET (core) applications

.UseSerilog((ctx, config) =>
{
	// Ensure HttpContextAccessor is accessible
	var httpAccessor = ctx.Configuration.Get<HttpContextAccessor>();

	config
		.ReadFrom.Configuration(ctx.Configuration)
		.Enrich.WithEcsHttpContext(httpAccessor)
		.WriteTo.Async(a => a.Console(new EcsTextFormatter()));
})

The WithEcsHttpContext ensures logs will be enriched with HttpContext data.

An example of the output is given below:

{
  "@timestamp": "2019-11-22T14:59:02.5903135+11:00",
  "log.level": "Information",
  "message": "Log message",
  "ecs": {
    "version": "1.4.0"
  },
  "event": {
    "severity": 0,
    "timezone": "AUS Eastern Standard Time",
    "created": "2019-11-22T14:59:02.5903135+11:00"
  },
  "log": {
    "logger": "Elastic.CommonSchema.Serilog"
  },
  "process": {
    "thread": {
      "id": 1
    },
    "executable": "System.Threading.ExecutionContext"
  }
}

This formatter also allows you to set ECS fields directly from the message template using properties that adhere to the https://messagetemplates.org/ format.

The available ECS message template properties are listed under LogTemplateProperties.* e.g LogTemplateProperties.TraceId

Log.Information("The time is {TraceId}", "my-trace-id");

Will override trace.id on the resulting ECS json document.