I am a linux user but we have requirement in our organization to create some partitions on solaris as following

/arch1 5GB
/backup 5GB
/ctrl 512MB
/index 30GB
/index1 15GB
/oradata 55GB
/oradata1 140GB
/redo 2GB
/temp 25GB

How do I create a partitions on solaris? and How can I format those partitions? What should I do for permanent mounting?

This, and your other posts, appear to indicate that you're also unfamiliar with Google, or in how to ask an intelligent question. First, Solaris is NOT Linux. Second, what kind of partitions (LVM, etc.)??

Read the man pages for the "format", "newfs", "fsck", and "mount" commands. For permanent mounting, put the devices into the /etc/vfstab file, where you'll see other devices already present. Again, read the man pages, and check Google.

what if the server is attached to external storage??

Nobody's perfect
There aren't partitions but file systems. The simpler way to fulfill the requirements would be to use ZFS.That depends on the architecture (x86 or SPARC) and the volume management software used, if any.
That depends on the file system used (UFS, VXFS, ZFS, ...).
Either add the new file systems to /etc/vfstab or do nothing, if using ZFS.

A SAN or a NAS ?

Ok, so what?? It's a disk...again, read the man pages for the commands given to you.

And AGAIN, how about answering things that are asked of you? What kind of storage, version of Solaris, etc. Don't just post questions and not answer/acknowledge posts.

As jlliagre indicated, it all depends . . .

You could help us help you by telling what kind of server, which version of Solaris, what external drive device and drives, etc., with enough detail to make it clear what you are dealing with. Just for example, if it happens to be a StorageTek then you may need to figure out how to use the Common Array Manager software (sscs at the command line) before you even get to the point of setting up anything like partitions. If it happens to be a J series JBOD, then it is more nearly plug and play. But you still need to decide how to deal with the file system. ZFS is definitely the way to go most of the time nowadays. Then you don't have to worry about partitioning, newfs, mount, /etc/vfstab, etc., and you gain lots of flexibility and functionality.

If you are a Linux user and your organization has no Solaris admin and is handing it to you, then you should expect to spend a fair bit of time with the appropriate online Systems Administration Guides.