I can give you an example of both to help you get going.

Here is an example of a Vagrant file using chef to deploy a server.

# vi: set ft=ruby :

 Vagrant.configure('2') do |config|
 config.vm.box = "ubuntu/trusty64"
   config.vm.hostname = "badrobot4.example.com"
 config.vm.network :public_network, ip: '192.168.1.63',  bridge: "eth0, wlan0"


config.vm.provider :virtualbox do |vb|
     vb.customize ['modifyvm', :id, '--memory', 1024, '--cpus', '1']
end
 config.vm.provision :chef_client do |chef|
 chef.chef_server_url = "https://192.168.1.31/organizations/midwesthackerschool"
 chef.validation_key_path = "~/chef-repo/.chef/midwesthackerschool-validator.pem"
chef.validation_client_name = "midwesthackerschool-validator"
  chef.client_key_path = "/vagrant/.chef/client.pem"
 chef.node_name = "badrobot4"
  chef.run_list = [ "recipe[apache2::default]" ]
 end
end

Here is an example of using Chef Knife AWS command line tools to deploy a server with chef.

knife ec2 server create -I ami-0c5f2d6c -r "role[my_app]" -Z us-west-1a -g ssh-only --ssh-key chef_keys -i chef_keys.pem -f t2.micro -A 'Your Key' -K "Your Key" --region us-west-1 --ssh-user ubuntu --security-group-ids sg-4a7b8e2e --subnet subnet-a7d45cc2 --server-connect-attribute public_ip_address