How do I define methods in a Mongoose model?

You didn't specify whether you were looking to define class or instance methods. Since others have covered instance methods, here's how you'd define a class/static method:

animalSchema.statics.findByName = function (name, cb) {
    return this.find({ 
        name: new RegExp(name, 'i') 
    }, cb);
}

Hmm - I think your code should be looking more like this:

var mongoose = require('mongoose'),
    Schema = mongoose.Schema,
    ObjectId = Schema.ObjectId;

var threeTaps = require '../modules/threeTaps';


var LocationSchema = new Schema ({
   latitude: String,
   longitude: String,
   locationText: String
});


LocationSchema.methods.testFunc = function testFunc(params, callback) {
  //implementation code goes here
}

mongoose.model('Location', LocationSchema);
module.exports = mongoose.model('Location');

Then your calling code can require the above module and instantiate the model like this:

 var Location = require('model file');
 var aLocation = new Location();

and access your method like this:

  aLocation.testFunc(params, function() { //handle callback here });

See the Mongoose docs on methods

var animalSchema = new Schema({ name: String, type: String });

animalSchema.methods.findSimilarTypes = function (cb) {
  return this.model('Animal').find({ type: this.type }, cb);
}

Location.methods.testFunc = (callback) ->
  console.log 'in test'

should be

LocationSchema.methods.testFunc = (callback) ->
  console.log 'in test'

The methods have to be a part of the schema. Not the model.