The API Guide gives a couple of examples of using EntityQuery, just with different entities. The following is updated from the example for ContactPerson, which has a parent relationship with Customer.
The key is knowing what field defines the relationship; for tasks it's "ParentProject", which isn't listed in the documentation, but is listed as a standard field in the Settings Customization screens.
Of course, you don't need to have stored/hard-coded the project's uuid, just look up the Project by Name or other attribute using another EntityQuery. You can retrieve the matching EntityId(s) from QueryResult.Entities.
I haven't figured out a way to directly query the uuid (EntityId.Value) as an attribute of a query.
string projectId = "210a7ced-a440-45cd-9a30-1ff251b2b1fd";
EntityQuery query = new EntityQuery();
query.TypeName = "Task";
query.Fields = new string[] { "Name", "StartDate" };
Compare condition = new Compare();
condition.LeftExpression = new FieldExpression() { FieldName = "ParentProject" };
condition.Operator = Operator.Equal;
condition.RightExpression = new ConstantExpression() { Value = new EntityId {
TypeName = "Project", Value = projectId } };
query.Where = condition;
QueryResult result = client.Query(query);