How can I catch Raikou in Pokémon crystal?

Find a route where you can enter and leave the route with nearby grass. (Ecruteak City is a good start since by the south side of this city has nearby grass). Take about 20 steps in the grass with the repel. If no Pokemon appear, Raikou or Entei are not there leave the area and come back.

Once you find it put it to sleep, if you try to trap it it will just roar you away. If you want to avoid other random encounters, you could use something like a level 39 haunter/gengar or jynx with a sleep move first in your team, and use repels so that everything below that level will stay away from you. It will be easier to find after you've found it once. Another way is to use a golbat, weaken it, and use mean look.