First make sure you are in hardcore mode.
Now there's two ways to get this, the dangerous way, or the safe way.
The dangerous way is to play the game straight (or even try using a wizard). The safe way is to grind a bit, at the right places.
First choose a good class, I'll recommend the crusader, he has a ton of ways to heal his life, and can take a lot of hits. When you get the templar follower don't change. The templar is a healer, and that's what you want. Steed charge is very good at escaping from danger, and finally there's the Indestructable rune. Which gives you 5 seconds of invincibility if you take fatal damage, this allows you to escape the worst situations (or quit the game if you want).
It doesn't matter what your class is, but that's what I found to be the best.
Now to level, you can do this almost any way you want, but the best way is to grind. What I did was beat the skeleton king (one of the first bosses in the game). After you kill him, continue til you talk to Cain after (do this to get extra EXP). Once you talk to him quit the game and then go to quest selection and choose quest No. 4. Reign of the Black King > The Royal crypt. Go to the waypoint and choose Cathedral Level 3 (it defaults to that). Then work your way to the Skeleton king and kill him again, continuing til you talk to Cain to get the second reward.
If you are doing it on expert this should take under 30 minutes a run (I was able to get it around 15 minutes if I found the right path) Playing on Expert got me 2 levels almost every run til I was level 25. I started at around level 15. Those 10 extra levels gave me so much power I could run the rest of the game with out a lot of danger.
From that point I had Akurat's champion which made boss fights simple. Just play smart after this point (or keep running it to grind up your levels, and you should be able to reach 70 easily, or you can grind other areas of the game for levels.