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Hello Ron,

we have a section in our documentation on how you can usually manage this scenario.

However, since you are upgrading between two major versions of Joomla, I strongly suggest you to do some practice locally.
First of all backup your site and create two clones.
Then on site 1 you perform some modifications you are expected to happen (new articles, new users etc etc).
On site 2 perform the update to version 3.4. Then backup site 2 and do a partial restore on site 1 and double check if everything goes right; you can find the instructions in the linked doc.

Beware: most likely the first times you'll break your site, it takes some practice.

Another way is the good old manual way: upgrade locally, note down all the changes you had to do, put your remote site offline, perform the same changes on your site.