Identify the uuid of the disk you want to attach but also the uuid of the target machine.

You can get the uuid disks with xe vdi-list or even with lvscan.
The VM's uuid you can get in many ways. One of them is:

[root@xengz ~]# xe vm-list params=uuid name-label=debian
uuid ( RO)    : 36f3763b-4011-055f-4945-92fe13a0027b

So, once you have all that you need, you can proceed.
In our example below, we will attach the vdi with uuid 3950c41a-39ef-439f-bd02-a6e346a60b99 to debian vm with uuid 36f3763b-4011-055f-4945-92fe13a0027b.

List the vm's disks before the operation:

As you can see, for each vdi you have a vbd. As a side note, when you want to boot from any medium (disk or cd), the target uuid is the vbd one.

[root@XenGz ~]# xe vm-disk-list vm="debian"
Disk 0 VBD:
uuid ( RO)             : 20b45191-8a7c-1c97-8995-8b1776866965
    vm-name-label ( RO): debian
       userdevice ( RW): 0


Disk 0 VDI:
uuid ( RO)             : 60a0f79f-2158-4d4b-8eba-8684d4197373
       name-label ( RW): 0
    sr-name-label ( RO): Local storage
     virtual-size ( RO): 8589934592

Create the corresponding vbd for the vdi and then list again the vm's disks:

[root@XenGz ~]# xe vbd-create vm-uuid=36f3763b-4011-055f-4945-92fe13a0027b device=1 vdi-uuid=3950c41a-39ef-439f-bd02-a6e346a60b99 bootable=false mode=RW type=Disk
2acbffca-fb41-b41f-a66e-3e403ad5aeb5
[root@XenGz ~]# xe vm-disk-list vm="debian"
Disk 0 VBD:
uuid ( RO)             : 2acbffca-fb41-b41f-a66e-3e403ad5aeb5
    vm-name-label ( RO): debian
       userdevice ( RW): 1


Disk 0 VDI:
uuid ( RO)             : 3950c41a-39ef-439f-bd02-a6e346a60b99
       name-label ( RW): 0
    sr-name-label ( RO): Local storage
     virtual-size ( RO): 53687091200

Disk 1 VBD:
uuid ( RO)             : 20b45191-8a7c-1c97-8995-8b1776866965
    vm-name-label ( RO): debian
       userdevice ( RW): 0


Disk 1 VDI:
uuid ( RO)             : 60a0f79f-2158-4d4b-8eba-8684d4197373
       name-label ( RW): 0
    sr-name-label ( RO): Local storage
     virtual-size ( RO): 8589934592

Once you have this done and you are sure the disk is not used, you can plug it in:

[root@XenGz ~]# xe vbd-plug uuid=2acbffca-fb41-b41f-a66e-3e403ad5aeb5
[root@XenGz ~]#

After this command, you will be able to see the disk in debian vm, without reboot.