It will vary for everyone to some degree.
For me it's a constant sensation of feeling drunk/drugged. I feel like I am removed from my body and mind. I can't properly process time, distance or my surroundings the way I used to. I have greatly impaired memory and concentration. I'm always tired and feel like I'm off-balance. My mind is forever wandering and never in the present moment. I can't focus on things properly, and can't absorb information such as reading long passages of text or following everyday conversations. I'm so absent-minded that I can say something and literally seconds later forget what I just said. If I go outside for a cigarette, I will come back in and don't really remember any of it happening. It's as if I am blacking out all throughout the day, and that life is just passing me by. Daily activities are difficult and even leisurely things don't feel the same. Walking around and doing basic things like going to the store are very draining, because I'm just sort of bumbling around in a fatigued, semi-dizzy state while my surroundings feel like an unfamiliar blur. It's as if I've been hit with a never-ending tranquilizer dart. Along with this, I developed what I call jelly legs, and have occasionally even gone through my knees, and have also passed out a couple of times.
My vision tends to swim, and I am prone to sensory overload when simply going to places like the supermarket and seeing all the various products lined up in the aisles, because my senses just perceive huge swaths of color and things I can't fully process. My sense of time is all off. I often lose time, and have no idea where certain hours/days/weeks went. I don't have a firm grasp of a chronology of events in my life. Something that happened earlier in the day will feel like it was a week ago - if I even remember it at all. Something that felt like it happened a week ago could've happened a month ago for all I know. It feels like I have a certain form of dementia, although logically I know I don't. However, I often worry that this is a precursor to it, because of how impaired I feel.
Heat, stress, physical overexertion, walking on uneven surfaces, fluorescent lighting and busy places with lots of people seem to exacerbate all of the above.
When I first came down with DP, I had excruciating anxiety. Quite simply the worst thing I've ever felt. Terrified and crying all day every day for no good reason. I developed migraines, major insomnia, and huge bouts of soul-crushing OCD as well. At one point I became suicidal and checked myself into hospital. That was when I got referred to an intensive outpatient program. The meds they gave me have kept these particular symptoms at bay, but the rest remain.
Ultimately I still don't understand this condition and struggle with it 24/7 as the symptoms I described in the first two paragraphs are constant and have been for years now. I don't understand the processes that are causing me to feel this way, and the lack of knowledge from anyone else regarding this condition is perhaps scariest of all.