When playing as Olaf you want to have Health as much as possible so that you can last in battle for a long time, so for items you take first Doran's Shield and sell it after, then you go for Berserker's Greaves and rush for a Warmog's Armor, then take Atma's Impaler for more damage then take Frozen Mallet, Stark's Fervor and Youmuu's Ghostblade.
For skills take Undertow and max it last then take Vicious Strikes and max it on level 15 and Reckless Swing and max it first. With Olaf it is so easy to farm just keep your enemies away whit undertow. If you chose to go on first blood chose your target attack him and follow whit undertow. When you get into a team fight activate Ragnarok which will make your enemies impossible to deal any damage to you, keep activating Vicious Strikes and follow whit Reckless Swing. Olaf's passive gives increases his attack speed for health each percent of health missing which can be very useful in 1 on 1 fights.
If you chose to go solo lane, just stay at the turret and try to kill minions, wait for one of your enemies in the lane to go for a gank and just kill the other one slowing him with Undertow and Exhaust picking up the kill with Reckless Swing.
When in team fights activate your ultimate so that you can take damage for your team which wont affect on you to much cause you will still have a lot of health keep striking whit your abilities and hope that your team is dealing damage too.