The ideal way to do it was to leave the old o-rings in place and starting by removing the farther away o-ring first so it could be slid over the old o-rings and not get it stuck in some other o-ring groove. This is in case you needed to save the used o-ring as reference to get a new one. If you already have the new o-rings it would be easier to cut them to remove them. Then, you could slide a new o-ring over the shaft, or stem, and over the old o-rings and this new o-ring would not fall in the incorrect o-ring grooves. Then you would do the second farther away o-ring and so on.
If you already removed all the o-rings either consider reinstalling the old ones so you can slide the new ones over them. Otherwise, clean the shaft with solvent to remove any oil and cover the grooves with masking tape or any suitable tape and try to slide the o-rings over the tape. Also, shrink tubing of suitable size can be put over the empty grooves and heated so it covers these grooves tight and remove them when installing the next o-ring. The tubing may sink into the groove a little but still you should be able to push the o-ring over the groove.
Or, start by installing the new o-rings by installing first the one closer to the beginning of the shaft and slide aditional (and further away) o-rings over the new o-rings. Anyway, you should use oil or grease to slide the o-rings. O-rings stretch enough that they can be slid over the new o-rings.
To install the o-rings over the beginning (or end) of the shaft, you should use an o-ring pick with the hook shape. Hold the o-ring over the shaft end with a finger and with the pick stretch the o-ring over the shaft a little until you get it completely over the shaft.