1. Nameserver Point: This is probably the more common way to point a domain. The only reason that you would not use this method is if you have existing email accounts. When you point your domain name via nameservers, it points the mail (MX) records as well resulting in your email not working.
2. CNAME Point: This is the type of domain point you'll want to do if you have email accounts created and do not want to move your email service elsewhere.
It sounds like you'll be doing a CNAME Point since you have an IP Address. You update your domains information from within your online account.
When you sign in, click Domains on the left hand side and click the blue Advanced DNS Settings link under listed under your domain name.
Update the necessary fields (sounds like A Records) and delete any existing records for which you're updating (ie if you're adding A Records, delete any existing A records).
Double check with your new website host about which records you need to update, A Records, CNAMES, or both.
I hope this info helps, let me know if you need further assistance.