It appears that you need 1/6 (17%) of wine or grape juice to still be able to say hagefen. The issue is that wine nowadays is already diluted. The proper way therefore appears to be to first say the blessing hagefen on the undiluted grape juice or wine then drink the mix (water drunk after hagefen doesn't require a separate blessing).
Sources:
Aish writes
Wine that is watered down retains the bracha
When diluted, grape juice easily loses its distinctive taste.
Therefore, when diluting grape juice with any significant amount of
water you can no longer say [hagefen].
In practice, since it can be difficult to determine whether or not the
taste of wine or grape juice has been significantly diminished when
diluted, it is recommended that you say Ha'gafen on non-diluted wine
or grape juice before drinking the diluted beverage.
PracticalHalacha writes
Say borei pri ha'gafen on drinks of wine or grape juice mixed with
water if at least 1/7th of the total volume is wine (or grape juice)
but the mixture but also still be considered to be wine or grape
juice.
Not everyone agrees with the above, see e.g., dinonline
Some authorities are stringent with regard to grape juice (unlike
wine), and maintain that if grape juice is diluted with water it loses
the Borei Peri HaGafen blessing. Although other authorities are
lenient concerning adding a small amount, this will only be true
insofar as the grape juice retains its principle taste and strength
[...] See Shut Minchas Shlomo no. 4, who is particularly stringent
concerning adding water to grape juice; a similar ruling has been
given by Rav Elyashiv z”l.
See more sources and details from Shulchan Aruch Harav here and KSA 49:3.
Note this is only for Ashkenazim, Sefaradim pasken differently (I believe using 50% instead of 1/6).
