OOC - General Out of Character thread
When you gain a level, instead of becoming a Rogue 2, you would instead become a Rogue 1/Ranger 1.
There's a table on page 163 that shows you what's required to multiclass into each class. The Ranger requires you to have a 13 in both Dexterity and Wisdom (so you need to swap some ability scores around), and the table on the following page shows you what proficiencies you gain from that class. In the case of Ranger, that would be "Light armor, medium armor, shields, simple weapons, martial weapons, one skill from the class’s skill list". You also gain all of the abilities/spells of that class for the level (Favored Enemy and Natural Explorer, but no spells, in the Ranger's case).
Roleplaying the Ranger multiclass would be pretty easy, as it's very similar to Rogue to start with. Taking a background that's related to Ranger'ish things works well for that (Outlander, Hermit, Soldier, Criminal (Spy)). Multiclassing from one non-caster class into another is really fairly straightforward, as is going from caster to caster. Mixing the two types of classes together is where things can get a bit more hairy.