Inspiration is hard to come by, but Drake has said many times that he can't write without the music. If you want to rap like Drake, you first have to live a little! Rap is a music that comes from true experience, and so you have to live to the fullest, maybe getting out of your comfort zone, to have experiences that are worthy of being written about!
As you expand your life experience, make sure you get around good people. Drake has said that the girls he met when he was playing on the biggest show in Canada, Degrassi, have influenced him in his rap career. That's probably why girls love his decidely raunchy stuff, because it's still delivered with an understanding for what women really want.
After you make sure your life is surrounded with great people, we get down to the actual technique of rapping. Rappers like Drake are well known for being able to freestyle, that is, rhyme off the top of the head to a beat. Inspiration for these freestyles come from their immediate surroundings. Practice not just observing your surroundings, but making songs about them. Freestyling these days can include written rhymes. Carry a pad and pen and write whenever your muse hits. Write in easy rhymed couplets at first.
Now it's time to put rhymes to a beat. Rappers like Drake, Kanye West, and even 50 Cent begin their careers with mixtapes, which is basically stealing other popular beats and reworking the lyrics from the original into their own. Take your pad rhymes and grab a Youtube instrumental of a song that you like. See how your rhymes fit. Don't quite just yet? It's ok. It's your first time. Step 5 is to repeat until you find your unique rhythm, like Drake.