I'd peel and chop into squares whatever I was using (provided it had skins to be peeled, like sweet potatoes or butternut squash) and then place it a pot of water and bring it to a boil. Once the cubes were tender, I'd drain it (but save some of the water) and then blend them with a hand blender.
Claire's age depended on the amount of water I'd put in. When she was first starting out, I'd put quite a bit of water in so it was more soupy and easier for her to eat. The older she got, the less water I'd put in. Then I'd let it cool for a bit and the spoon it into ice cube trays. Once frozen I'd transfer them to Ziploc Freezer Bags, and write the date on them so I knew which ones to use first.