Drains were daunting to me too and from what I gather they vary a fair bit between different people and types of surgeries as to where they're placed and how many are used.
I had lymph nodes removed two weeks ago and had two drains on the right side. My breast care nurse gave me a carry bag so I kept the bulky collection parts of the drains in the bag that I carried on the opposite shoulder. That might not be a suitable solution depending on type of surgery but they will have solutions for you.
I was wary as I pottered about to keep the tubes from getting caught on things. People thought I was weird for fussing - they reassured me that the tubes were stitched to me! Eek. I hadn't expected that at all.
When I got home, community nurses visited me. They changed the collection bags on the drains a few times and showed me I could use a permanent marker to mark off how much fluid had collected in a day. One drain was removed after 6 days, the other was removed one day later.
I was a bit cranky and sleep deprived while the drains were in because I don't think I slept solidly worrying over them. I was relieved once they came out, it felt freeing.
6 days now since the second came out and I still occasionally pause before I get up from a chair thinking I need to check where the tubes are :)
My short version: I just had to carry the drains around. The hospital provided information and made supports available to manage the drains once I went home.