Windows Server 2008 R2 Create a User Account and make the account a local admin.

You can try to disable the User Account Control as this is a system wide setting for all users every time users installs a program.

You can follow this link: Turn off UAC for Windows Server 2008 R2

Local admin rights to what?  Every machine, a specific one?

If you want it to be an local admin of every machine, the user either needs to be a member of a group that is already a member of the local Administrators group (like Domain Admins), or you can define the membership of the local Administrators group using group policy, where you would configure the "Restricted Groups" setting and make the user a member.

You're not clear about what you're trying to do.

Are you trying to make a DOMAIN USER a member of the LOCAL ADMINS on a DOMAIN CONTROLLER?  If so, you CANNOT - there are no local accounts or groups on a DC.  For the user to have admin access, they need to be a domain admin.

Are you trying to make a DOMAIN USER a member of the LOCAL ADMINS on a SERVER or a WORKSTATION?  If so, then you need to put the user account in the local admins group of the machine in Computer Management.  

NOTE: once a user is in that group, they MUST logout and login again before the credentials take effect - when a user logs in a token is generated indicating what groups they are a member of - it is NOT updated.  So if you add them to the admin group, it won't take effect until they log out and log back in, generating a new token.  (A reboot, obviously) also works.

The advice to disable UAC is, in my opinion, VERY POOR - Disabling UAC, even for an experienced admin should NOT BE DONE unless it's the only possible option.

The advice to disable UAC is, in my opinion, VERY POOR - Disabling UAC, even for an experienced admin should NOT BE DONE unless it's the only possible option.

This is true but there is another way of doing it without disabling entirely. To allow admins to have a disabled UAC, you can use the group policy editor to change the settings to a: " Change this setting to Elevate Without Prompting to provide administrative privileges automatically" so that it will not be disabled to users without admin privileges.

This is the node for the policy settings: Computer Confguration\Policies\Windows Settings\Security Settings\Local Policies \Security Options

Based on your reply, if you do have set the Security settings in the server, you may have to add domain admins into the administrators on each remote machine. It will have this user in the remote PC: "DOMAIN/DomainUser" format in order for the securities to take effect. Re-login and test.

Still not clear to me.

What I'm trying to accomplish is to Make a Domain User on a Server  have Administrator Privliages

Is the Server a Domain Controller or a Member Server?  This is hugely important and you're not telling us so far.

Every time lets say a Flash update comes up it would promp that the current user does not have sufficient Privliages to execute command.

What does this have to do with your previously stated goal (quoted first)?  Do you have Flash installed on the server?!?!?!?  RDP shouldn't care who runs it so the fact they are getting prompted for admin rights to do a flash update should be irrelevant.  UNLESS Flash is on the server.  In which case, AGAIN, IS THE SERVER A DC?

Pictures help A LOT!  Take some screen shots and post them.

As per your requirement, you have to add a user to local administrators group on that specific server.

Open server manager in server, then add that AD user in "Administrators" group and then....
that's all.

I'm having trouble understanding you.  First you said

...when that user is  logging in from a remote computer...

which to me means that you are using a RDP connection from a remote computer to the server you're asking about.  But then you say

...I don't want to RDP...

Next, you say

When joining a Terminal PC ( located in another office) to a Domain Controller the user account in the active directory sets the permissions on that Terminal.

I just don't know how to interpret this.  I assume by Terminal PC you're not referring to a Terminal Server, but just something like a standard workstation.  But what do you mean by "joining" - joining to the domain, or just logging on to it?

However, maybe the fact that I don't understand what you're describing isn't important.  If this is a domain controller, any user that is a member of BuiltIn\Administrators should not encounter a prompt for any other credentials, though I would strongly advise that only Domain Admins should be allowed administrative permissions on any DC.  For any other workstations or servers that are members of the domain, it has already been mentioned how to make a domain user an administrator of that computer.