If you are staying around Lake Naivasha or Naivasha town, it is very easy to visit Mount Longonot National Park without paying for an expensive tour.
To get to Lake Naivasha, I took a one-day safari tour from Nairobi to Lake Nakuru. I arranged for them to drop me off after the Nakuru safari at Burch's Resort at Lake Naivasha. The hotel is very close to the main road back to Nairobi. The safari tours coming from the Maasai Mara Reserve and going to Lake Nakuru also pass Naivasha and can drop people off.
If you are not on another tour to the area, you can take a matatu minibus from Nairobi to Naivasha. The matatus leave frequently from the city center bus area at Map Location: -1.284842, 36.830737 and are very cheap.
From Lake Naivasha or Naivasha town to the national park entrance gate is about 25 kms. It is best to take a ride share or taxi because the entrance is about four kms from the main road. I recommend Nathan the Safiri driver. He will charge whatever Safiri app shows. You can call him directly to arrange transportation at +254 724 678 510 (international SIM) or 0724 678 510 (Kenya SIM).
The park entry fee is 26 USD and a guide is not required since there is only one, easy to follow trail.
The moderately steep hike to the volcano crater takes about an hour. There is a trail around the crater that is mostly flat but is very challenging at the two high points. It takes two to three hours to circumnavigate.