Assuming the machine is completely empty, the steps would be approximately
as follows :

First you have to restore the root volume group including the ADSM
software.
On AIX, this is best done if you have a complete mksysb backup of the
rootvg
you can restore.

When you have the rootvg installed and ADSM working, the next step is to
remake the other volume groups and the filesystems residing on those volume
groups.

If you only have one VG and one or a few filesystems, you may just do that
manually,
but if you have many VGs or your configuration is more comprehensive or
complicated,
you'll want to find a way to automate this.

There are more ways you can do this.

One way is to simply have a script written that will do the work, but then
you have to constantly
maintain that script every time you make a change to something in the FS or
VG area.

A better way is to utilize the restvg command, which will remake a volume
group and restore
the files in the VG from a traditionally backup made by savevg command.
Savevg works by creating some files in /tmp/vgdata where it will create a
directory for your
volume group with the name of your VG, e.g. /tmp/vgdata/myvg.
In this directory, savevg will place 2 files, one called myvg.data which
contains (look in it!) the
data about LV names and sizes and all the other stuff about the VG.
The other file is called filesystems and contains the data about the
filesystems on your machine.
A third file in /tmp/vgdata points to those 2 files mentioned above.
Those 3 files, together with the actual filedata from the filesystems will
be written to a backup file or
tape.
But since you have backed up your files with ADSM and not with savevg, you
cannot or rather do
not want to, have actual data restored by restvg, but you only want to have
the volume group
created and the filesystems created.
The way to accomplish this, is to make a savevg with no data. There is a
parameter on savevg that
will let you use an exclude file, so use an excludefile that excludes all
data in the volumegroup.
You then have a backup that contains all the nessecary information about
the volumegroup and filesystems,
but with no actual data.
You can the use restvg to remake the volumegroup and filesystems for you.
After this is done for all your volumegroups (except rootvg!) you should
now have all your filesystems
ready for ADSM to restore data into ....

Now, this method only works if you have created the empty savevg backups
prior to the situation
where you need them, so you may want to automate this process by running a
script every night
that does this for you.
If you have not done this and need to restore, I presently do not know how
you can do this without
manually creating the volume groups and filesystems.
You may need to read the man pages for savevg and restvg and maybe also
look in the savevg and
restvg scripts themselves (they are readable scripts).
Also, testing this procedure before you actually need it is obviously also
a good idea.

I've been told there may,( I say may because I have not looked into it
yet), be a way to do a similar thing
with the Disaster recovery Module in ADSM.

Regards

Peter