It is not reasonable to have as your goal "avoid all hurt feelings in the other party". They are going to be hurt, they have a right to be hurt, and there is no magic formula that will get them to agree with you that splitting up is in their best interests. So your goal is to minimise unnecessary hurt. You can do this by:
Use "I" statements - "I don't want to be in this relationship any more, my feelings have changed, etc." Don't list their faults or tell them ways in which they don't measure up. Make it about YOU and your feelings.
They may want to know why - there is no answer you can give to this that will be satisfactory (since the subconscious goal is to "prove" that your reasons aren't good enough so that you have to stay). Tell them you don't know why and repeat that your feelings have changed and you don't want to be in this relationship any more.
Be very clear - don't make vague statements about "not knowing where to go from here" or "needing time". The relationship is over, starting right now.
Don't try to get the other party to agree that they will be happier in the long run, splitting up is in their best interests, you're doing them a favour, etc. This may very well be true, but they will be in no mood to see it and will (rightly) perceive this as an attempt to make yourself feel better. Leave out any hint of "it's for your own good" and stick to the "I" stuff.
Have some practical plans in place - if you live together, one or both of you will need somewhere else to live. If you have joint property, one will need to buy the other out. You don't need to have your bags packed and hidden under the bed, but you do need a plan for what happens immediately after - you going to stay with a friend or family member for a few days, for example.
Don't get drawn into a discussion of future plans you have together - a holiday, a friend's wedding, etc. All of these things ultimately don't matter.
Good luck, OP. It's never a nice thing, but it has to be done.