The term for “plain” non-flavored ice cream

The softness of ice cream is going to depend on a variety of factors:

Use of gums and other binding agents, amount of sugar, the amount of fat, and especially the amount of "overrun" (air) that is churned into it during the freezing process. Less expensive ice creams will usually have a softer "chewier" texture than premium ice creams due to more gums and a great amount of air being churned into it to increase volume.

More air = more volume = more yield for the same amount of ingredients used.

Preface: I'm not a big fan of fruit-flavored stuff (I like fresh fruit by itself, just not in stuff...) so I can't speak to these from personal experience.

• For fresh fruit, puree in a blender or similar. Moist fruits can probably be pureed in their own juices; otherwise, you'll need to add some. You'll probably want to add some sugar, but offset this by reducing the sugar you add to the ice cream mix. (Seeds might be an issue too - get seedless if possible.)
• As Manako suggested, you can also cook it down and then puree, though this will result in a wetter mixture than with their natural juices alone. This will also present a different flavor profile from the fresh fruit, so experiment to find what you like.
• Another possibility would be to cook out some of the water from your puree.
• In any case, you'll want to reduce the liquid ingredients of your normal recipe by roughly the same amount as the pureed fruit you're adding.
• In light of the previous item, you'll probably want to use a higher-fat cream than normal, since the fruit will add a lot of water.
• Unlike "chunky" additions, you don't really care that the ice cream should be at a thick consistency before you add them. (for suspension) I'd just add it directly to the mix before you start churning.