Most of the heavier duty modern ones have screw options to fit into the sewing tables like the old ones. If you're unsure of what yours can do, find a sewing machine repair shop or JoAnns and ask them questions about your model and the one that you have. Sometimes you get lucky and find the one person in that shop that
actually knows everything.
And yes, start underneath. Make sure there is no needle on the foot (because God forbid...
) and that anything moderately loose is taken off before you do anything. It's good if you have an extra pair of hands handy because some models of table require stupid stuff. Like holding the carriage at a bad angle to relieve the pressure on the screws so adjustments can be made.