Advancing the RNG
There are a number of different ways to advance the RNG, but for capturing Pokémon the three easiest are Journal flips, walking where there are wild Pokémon present while using a Repel, and walking where there are no wild Pokémon.
Journal Flipping
Opening the Journal, or having it automatically open, when there is a caught or defeated Pokémon on the first page advances the RNG by 2. There are a number of formats for the caught/defeated Pokémon text. Those listed below have been verified to advance the RNG. 'Caught a female BIDOOF.'
'Caught AZELF (LATE NIGHT).'
'UXIE was caught (DAY).'
'Defeated a male BIDOOF.'
Flipping to a page in the Journal where a caught or defeated Pokémon is listed advances the RNG by two. The same message formats listed above will advance the RNG.
Walking in areas with no wild Pokémon
Taking 128 steps will advance the RNG by a number equal to the number of Pokémon in your party. This step counter is stored when you save your game and does not revert to zero when you soft reset, so it is important that you walk exactly 128 steps. Any more and it is possible that the RNG will advance again and throw off your calculations.
Walking in areas with wild Pokémon
The RNG is advanced by one for each step or turn that you make, even when Repel is in use. Turning and walking in a single movement advances the RNG by two.
Wandering NPCs
The preceding methods to advance the RNG were listed because they can be used, in a controlled manner, to reach a target frame. On the other hand, Wandering NPCs are discussed here because they tend to have the opposite effect: advancing the RNG in an unpredictable manner and foiling our attempts at hitting our target frame. The challenges that Wandering NPCs pose are not always insurmountable, though, and this information should be useful for working around them or at least knowing how to avoid them. It is noteworthy that if you are attempting to capture a legendary Pokémon there will be no wandering NPCs to deal with which means this information can be safely ignored. For those attempting to capture non-legendary Pokémon, read on.
Wandering NPCs are those who walk or turn in a random pattern. The best way to tell if the NPC is moving in a random pattern is to simply observe it. If, after a few moments, you can't predict the pattern of its movements it is a wandering NPC. All Wandering NPCs in a zone will advance the RNG even if they are not on the same screen as the player character; therefore, it is important to know if there are any at all in the particular zone where you are capturing a Pokémon. You can tell when you enter a new zone because a location box is briefly displayed showing the name of the zone.
One additional method to determine if there are wandering NPCs in a zone is to capture a Pokémon, without a synchronizer, after waiting approximately one minute following entry to the game world. Once this Pokémon is captured enter its stats into the "DPPt Seed Finder" of RNG Reporter, then generate a frame listing for method J. For Pokémon that were captured using Sweet Scent the frame will be two. For those that were not the frame will be close to the number of steps that were taken before encountering the Pokémon. If there are wandering NPCs the frame will generally be some number higher than 50.
If there are no wandering NPCs in the zone you will have no issues with unwanted RNG advancement. If there are you will want to figure out which can be stopped. Wandering NPCs may be stopped if they are able to be re-battled using the Vs. Seeker. To stop these wandering NPCs you must use the Vs. Seeker successfully and re-battle them. When the battle is over these NPCs will no longer wander (and will no longer advance the RNG) until you leave and re-enter the zone. This effect persists between resets of the game, making this a viable technique. Unfortunately, not all wandering NPCs can he stopped as they do not all accept rematches using the Vs. Seeker. Experiment to figure out which ones can in a particular zone.
Use any combination of these to advance the RNG. For even numbers it is recommended to use Journal flips exclusively. Divide the number of RNG advances that are required and divide that number by 2 for the number of Journal flips.
For odd numbers the easiest method is to have an odd number of Pokémon in your party and walk 128 steps on tiles where there are no wild Pokémon. After this subtract the number of Pokémon in your party from the number of required RNG advances and then divide this number by two to get the number of Journal flips that are required.