Make a request "Weather Deviation Required" and specify a distance off track to clear the weather and you will usually get approved. Jepp has a the whole drill including in the case ATC cannot approve the deviation, in which case, you deviate with a maneuver in altitude to provide the best clearance, using TCAS.
Suggest reading the whole Jepp version. The weather in the NAT region rarely requires deviations, but the Mid-Atlantic and Pacific are another story.
GF