I have just made my CPF nomination recently. As it is still fresh in my mind, the following is how the process went for me:
1). Head down to one of their CPF Service Centres (see here for a list of CPF Service Centres). I went with my nominee (The person/s who will be receiving your CPF monies if anything untoward happens to you).
2). Produce your NRIC to the staff, answer some questions related to the nomination (Name, NRIC, Nominee Name/s, Nominee NRIC/s, relationship to Nominee/s, marital status). Staff emphasized that any change in my marital status would require another new nomination to be made.
3). Wait, as the staff fills up the CPF nomination form on your behalf.
4). Verify that the information on the CPF nomination form is correct. Signs it.
5). Staff serving me signs as one of the witnesses. Staff informs me that another colleague would ask me some verification questions (my name, NRIC, nominee/s name, relationship to nominee/s). After the verification is completed, staff's colleague signs as the second witness.
6). Requested for a photocopy of the signed nomination form. Staff informs me that my nomination will be reflected on my CPF account in two weeks' time.
That's all. The entire process took around 10-15 minutes. Hope this is helpful for those who are wondering what the process is like. Cheers!