Well, for task like that, you have some choices...
1. ask odoo to do migration for you : https://migration.odoo.com/
2. check here : https://github.com/OpenUpgrade/OpenUpgrade
3. do it yourself.. 

It is not simple, or easy, especialy if you have some custom modules... 
But can be done.. 

Hope this hels :)

As Bole said,

The community OpenUpgrade is the only solution to migrate a database (unless you want to do it all yourself).  You will need to upgrade from 6.1 -> 7.0 and then from 7.0 -> 8.0.  If you have custom modules they will need to be upgrade by you or the original developer.  

If historical data is not important to you and they want to start fresh.  Some people have exported data in .CSV (Comma Separated Value) files and then imported them into Odoo v8.

Sadly, there are no easy solutions.

Thanks for the answers.

The plan is that my company wants to do the migation, without the use of the migration service. We are upgrading the custom modules, the problem we are facing now is the migration of the information from the tables of the database from 6.1 to 8.

I am testing if the etl model (https://github.com/ingadhoc/odoo-etl) can do the task.
Does anyone already tried to use it?
If so, do you have some feedback about it?