My trial in Houston was a stem cell infusion, just a single, one-time treatment. It required 3 weeks as an inpatient: 1 week before the infusion to run tests and do the chemo needed to prep for the stem cells, then 2 weeks of really close monitoring for adverse reactions. After discharge, 2 more weeks close to the hospital for further daily check-ups, and then allowed to return home. I was home for 2 weeks, then required to return for scans and blood tests, which indicated trial failure, so I was "let go" from the trial and returned to my previous chemo at home. If my blood and scan results had indicated any progress, I would have had to return at pre-determined intervals (6 weeks, then 12 weeks, then 18 weeks apart) for more scans and blood tests.
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Current treatment doesn't necessarily have to be failing in order to qualify for a trial. Just read the fine print in the exclusion/inclusion criteria for each one. Many explicitly state that you can participate if you've reached a point where you can't tolerate the current treatment even if it is working; worsening neuropathy is a classic example. Kidney sensitivity, bone marrow issues, vision, CNS, digestive, cardiac and pulmonary side effects are other valid reasons. It's a judgment call and a gamble if your current treatment is "sort of" working and "fairly tolerable" as was the case with mine. All the stars aligned just right for my trial (regarding insurance, time off work, a place to stay, a promising treatment that I actually qualified for, etc), but since the treatment didn't work, I wound up worse off than if I had just stayed on the previous SoC regimen.
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Regarding the travel requirements: They're likely different for every trial. I had other options that would've required me to be present only one day every three weeks for an infusion. They wanted me to stay close for another day in case of adverse reaction, but were fine with me flying home the second day after.
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As @stageivsurvivor mentions, there are resources like PanCan, LetsWinPC, TriCanHealth (and cancercommons.org?) who will do some of the legwork for you, but you are correct in that your current treating/consulting oncologist really has no explicit responsibility to help you find a trial. I find this to be sad and infuriating, but it is what it is...

I've had second-opinions consults at Mayo, Hopkins, Anderson, Cleveland Clinic, and Sarah Cannon, so I have a MyChart account and an "assigned oncologist" at each. When asked about trial options, none ever recommended one outside of trials going on at their own site. In fact, they didn't even seem to be aware of trials going on at other sites unless it was a trial they were already in negotiations to try and join for themselves. But being "in their system" does speed your access to them when you're searching.