When using Apricorn balls or Ancient pokeballs, the rules are the same. Apricorn balls retain their regular catch rates and Ancient Pokeballs catch at +20. (or -20, whichever one is bad)
For all other captures, you are required to have a piece of rope handy. Each capture operates at the same level as a great ball. The amount of rope required depends on the size of the pokemon, based on their weight class.
Weight Class 1: Three feet
2: five feet
3: Seven feet
4: Ten Feet
5: fifteen Feet
6: Twenty feet
Weight Class 1 – Any pokemon between 0 – 25 lbs; 0 – 11 kg
Weight Class 2 – Any pokemon between 25 – 55 lbs; 11 – 25 kg
Weight Class 3 – Any pokemon between 55 – 110 lbs; 25 – 50 kg
Weight Class 4 – Any pokemon between 110 – 220 lbs; 50 – 100 kg
Weight Class 5 – Any pokemon between 220 – 440 lbs; 100 – 200 kg
Weight Class 6 – Any pokemon heavier than 440 lbs; 200 kg
On a successful capture, the PC is assumed to have somehow used only the rope and his manly presence to capture the pokemon. The rope is then used up. On a botched capture, the pokemon is assumed to have broken its bonds, and the rope is destroyed.
Making a capture has a maximum range of three meters away. Any further away and a DEX check of 10 is required, with +1 to the DC for each meter away you are over three. Ranger Lasso Captures have a longer range more like a vanilla ranger, however, for normal captures they still need to follow the same rules as everyone else.
Some pokemon are special cases. Their captures either require more or less rope than the above weight classes, or can't be done with normal rope at all.
Ghosts: Ghosts and pokemon with Phasing cannot be caught with rope. They will phase through it, leaving the rope still useful for another capture.
Superstitions: You CAN capture ghosts by preying on superstitions. Lure a Gastly into a circle of table salt before making the capture roll. Have the Rotom look in a mirror and make the roll. If making a capture with a mirror, the pokemon will be tied to the mirror, similar to a pokeball. If the mirror breaks, it will stick around as a normal capture if it likes you, but may flee or attack if it does not.
Another way to catch ghosts is to set up a camera and take their photo. Inside combat it takes a full trainer action to set up the camera. After the camera is set up, you may take the Ghost's picture if you have line of sight. Roll 1d100 as normal. If the capture is successful, the pokemon will be trapped in the negative, and the picture must be developed for you to be able to summon the ghost.
Water Types: Water types and bug types can be caught using fishing nets, or butterfly nets as well as with rope. A big enough net is the ONLY way to catch a Wailord. When making a capture with a net against a Water or Bug type, subtract 5 from the capture roll.
Viscous Pokemon: Grimer, Muk, Ditto, and Slugma require finesse. They are all dangerous to the touch or are too slippery to tie up and thus cannot be caught using ropes. You must catch them in another way, either by enclosing them in a trap (If the trap is airtight, subtract 5. If not, add 5), or by otherwise causing it to stop moving while still being conscious. If the viscous nature of the pokemon is somehow subverted, say, by freezing it, you may make a capture roll with rope as normal.
Invisible Pokemon: When a pokemon is invisible, make an accuracy check of 6 before beginning the capture.
As usual, in lieu of capture, you may opt to try to befriend a pokemon instead. The rules for this are largely the same, although remember that these are still wild animals you're dealing with.