It is important to understand that;
Socialising your puppy does not mean that you throw your puppy into a number of new situations and hoping that they cope!
Socialising is m more than just attending a couple of puppy parties at the local vets.
Even if you have another dog, your puppy needs to be introduced to as many other dogs as possible too.
Instead, socialising your puppy should involve gradual introductions in as many new situations as possible in a positive and fun manner.
You need to expose your puppy to as many different environments, people and dogs as possible.
Puppies parties are a great starting point for this; your puppy will be exposed to many different puppies and people. However, puppies need to meet older dogs too - especially in that critical first 16 weeks so if you know any calm, friendly, fully vaccinated older dogs it is worth getting your new puppy to meet them too.
Introductions to other dogs need to be carried out in a calm manner, keeping your puppy on a lead and letting them sniff the older dog. This is an appropriate way for puppies to meet another dog. Many people advocate "letting the dogs sort it out for themselves" but such an approach can cause your puppy to become wary or fearful of older dogs - not the result we are aiming for!
The most important part of socialising your puppy is to introduce them to as many new things as possible in the first 16 weeks of your puppies life and to make these introductions as positive and fun as possible! Try for 100 new things in the first 100 days of their life!
If you puppy is showing nervousness or fear when exposed to new experiences it might be worth speaking with a qualified dog trainer to help coach you through this time with your puppy!