Common signs of a pet choking are them pawing at their mouth, wrenching and excessive drooling. If you can safely restrain your pet and fully open their mouth you can attempt to remove the object yourself. Always be as gentle as you can to prevent further damage, if the object does not come out easily, leave it alone and call for a vet immediately.
If your pet has swallowed any string or thread half way, then do not try to pull it out as it may be attached to their intestines. If they have swallowed a fishhook and it is stuck, take them to the vet, a fishhook is unlikely to cause the pet to suffocate.