By simply tapping into their beast's chakra, a jinchūriki begins their initial transformation. They are surrounded by a layer of red, wispy chakra and are granted enhanced strength, speed and healing. The beast's chakra supplements the jinchūriki's and they are able to manipulate the chakra to a certain extent: Utakata can form it into waves and blasts while Naruto can thrust it outwards with his fist or emit it as a roar. In this form, the jinchūriki's body undergoes slight physical changes. When Naruto enters this form, his eyes change colour and become slitted, and his nails and canine teeth grow longer and sharper. Naruto's hair also grows longer and spikier, and the whisker-like marks on his cheeks widen and thicken. In the anime, when Utakata entered this state, his eyes instead became a shade of yellow and he did not undergo any other physical changes. It is also possible for a jinchūriki to enter this state without chakra visibly emanating from them, instead just gaining the physical alterations.
Rather than fully transform into their respective beast, jinchūriki can isolate the transformation to parts of their body. Instead of appearing as clear or dark chakra, these partial transformations fully resemble the beast's, having fur, scales, etc.
In principle, all jinchūriki can fully transform into the tailed beast sealed within them when the seal breaks and they entirely lose control over the beast.