In the Harry Potter and the Order of the Phoenix, Harry, Ron, Hermione, Luna and Neville ride the thestrals to rescue Sirius. They do this after they were caught by Dolores Umbridge in her office.
Since the thestrals can be seen only by people who have seen death like Harry and Luna, how did they manage this?
Firstly, it's three of them who can see the Thestrals, not two. This is made clear in Harry Potter and the Order of the Phoenix chapter 21:
‘The only people who can see Thestrals,’ she said, ‘are people who have seen death.’
[…]
Professor Umbridge smiled indulgently at them and then turned to Neville.
’You can see Thestrals, Longbottom, can you?’ she said.
Neville nodded.
‘Who did you see die?’ she asked, her tone indifferent.
My … grandad,’ said Neville.
Chapter 34 describes the riding on Thestrals in detail. The other three students indeed have difficulties, but they manage with help.
Ron, Hermione and Ginny, however, were still standing motionless on spot, open-mouthed and staring.
‘What?’ he [Harry] said.
‘How're we supposed to get on?’ said Ron faintly. ‘When we can't see the things?’
‘Oh, it's easy,’ said Luna, sliding obligingly from her Thestral and marching over to him, Hermione and Ginny. ‘Come here …’
She pulled them over to the other Thestrals standing around and one by one managed to help them on to the back of their mount. All three looked extremely nervous as she wound their hands into their horse's mane and told them to grip tightly before she got back on to her own steed.
‘This is mad,’ Ron murmured, moving his free hand gingerly up and down his horse's neck. […]
After that each of them just have to hold on strong to the Thestral and it does the flying on its own. There's no need to control Thestrals, they find their own way.
‘This is bizarre!’ Harry barely heard Ron yell from somewhere behind him, and he imagined how it must feel to be speeding along at this height with no visible means of support.
Since the thestrals can be seen only by people who have seen death like Harry and Luna, how did they manage this?
They just can't see them. But they can ride on them.
In this scenario, they don't really have a choice. So they took the risk and held onto the thestrals. In the movie, one can clearly notice Ron being very scared mid way into the ride.
So they just held on to whatever bony structure they could feel, and held on tight for their life.
The DA was able to ride the threstrals because Luna and Harry helped them mount/dismount.
"Hermione looked as though she was glad to have two feet on solid ground, as Luna pulled her down by the hand in front of the telephone booth that Harry know was the entrance to the Ministry."
-Harry Potter and the Order of the Phoenix
This explains that Luna (and presumably Harry) helped them get on and off, and I also have another quote that describes them flying.
"Ron looked nervous, but also looked as if he was having time of his life. He probably felt like he was flying, [Harry] knew."
This means that they could still fly, but they were probably nervous (understandably so.) And mounting/dismounting also was not an issue.
