To become familiarized with KPop it might be helpful to check out the 3 big players in the industry: SM, JYP, and YG. Their artists are arguably the biggest and most well known idols. There are obviously other big name groups outside of these agencies but it may be a good starting point! Also start watching variety shows that feature idols as cast members or guests (Strong Heart, Running Man, Invincible Youth, We Got Married)! One thing I've found about KPop that differs from JPop is the amount of cross group interaction there is in the industry. So many shows have idol specials or feature a mix of idols in the cast. I've often fallen in love with idols on these shows before even hearing any of their music (Jo Kwon on WGM)!

Here are my faves from the aforementioned 3 big companies:

SM
Super Junior: You'll have A LOT of material to go through with these guys seeing how they've been around so long and have a number of sub-groups. They are also regulars on lots of variety shows. Totally loveable guys.
SNSD: Infectious songs with point perfect choreography. Watch their mega-hit Gee and other good ones to know are Genie, Oh, Run Devil Run. I always just find myself so mesmerized by them.

JYP

Wonder Girls: Debuted around the same time as SNSD and are right up their as one of the most well known girls groups in Korea. Haven't been in the spotlight much lately though because of their attempts at crossover in the states. Listen to Nobody, So Hot, and Tell Me
2AM: Ballad group with all 4 members having amazing voices. Watch Jo Kwon on We Got Married and you'll become a fan for sure.
2PM: Brother group to 2AM, their music is more upbeat and danceable. Cool choreography and smokin hot guys!
miss A: 4 member girl group. If you're familiar with dramas you probably know the maknae Suzy. Listen to Goodbye Baby and Bad Girl Good Girl

YG
BIGBANG: They've been around since 2006 and are a huge name in the industry. More urban feel for their music and style. They are directly involved with the composing and writing of their music which I think sets them apart from many groups. Listen to Haru Haru, Lies, Last Farewell, Tonight, and Fantastic Baby.
2NE1: Don't like cutesy cookie cutter girl groups? 2NE1 break the mold and are just awesomely unique in their style, fashion, and music. Listen to Fire, Can't Nobody, It Hurts, and I am the Best.

Some of my other favourites I recommend: BEAST, SISTAR, CNBlue, Infinite, and KARA

Most of the ones I've mentioned are the big names that have been around for a few years. I think it's a good place to start. The KPop scene is flooded with new rookies every year it gets hard to keep up!
Big Bang: Number 1, Hands up, Cafe, Gara Gara, Goodbye Baby (basically any Big Bang song is a good one, which is why there my favorite male K-pop group) Shinee is also really good, I don't think I saw Sherlock on the list, so you should check that out too. For girl groups my favorite is 2NE1: Clap your hands, fire, hurt, lonely, pretty boy, In the Club, I Love You (Again, basically you can't go wrong with any 2NE1 song either imo) Other good girl groups are F(x): La Cha Ta, Chu, Hot Summer 4Minute: I me mine, Huh (my favorite song of theirs!), Why, What a girl wants, First (Japanese) SNSD: Run Devil Run, Oh!, Genie, Gee The Wonder Girls: Tell me, Like This, Nobody, So HOT Also solo Artsit/ tracks: BoA (solo artist) is amazing!: Hurricane Venus, Eat you up, Energetic, girls on top Dara(from 2ne1) Kiss (it's one of my favorite solos! also idk if you like Lee Minho, but if you do he's in the MV, so bonus! lol) Daesung(from Big Bang): Baby Don't cry, Wings, Lunatic (This is from a drama he's in called What's Up if you like the song you should check out the drama too, because it's really good and the music rocks!!) seungri (from Big Bang): V.VIP, What should I do, Strong Baby
all of these have mvs (music videos), so try to watch them:) ss501: love ya, love like this, fighter, a song calling for you, warning (its their debut song, back from 2005), find, deja vu, unlock, oh all of their songs r awesome there r tons more check them out :) also check out their solos, their names r kim hyun joong, heo young saeng, kim kyu jong, park jung min and kim hyung jun... hihihi they r my fav so anything by them is awesome (it really is)... also check out these: dbsk/tvxq/jyj: mirotic, keep your head down, why did i fall in love with you (japanese), rising sun,... rain/bi (hes a solo singer, you must check him out): rainism, love song, in my bed, love story,... beast/b2st: soom, shock, bad girl,... and some random songs u should check out: sg wannabe: saldaga h.o.t: outside castle tree bicycle: one more time se7en: digital bounce davichi: dont say goodbye jang ri in & xiah junsu: timeless g.na: black and white narsha: bbi ri bba bba s.m. the ballad: hot times t-max: almost paradise trax: tell me your love a.n.jell: promise brian joo: bullet uff ill continue later...hope u like these so far +the stuff others mentioned:) also check out seoul.fm its basicly online radio and eat your kimchy for anything kpop & korea related
Here are a few from my all-time favourite groups - DB5K: Miduhyo (Believe), Rising Sun, One, O.Jung.Ban.Hap, Purple Line (Japanese/Korean Ver.), Mirotic, Love In The Ice (Japanese/Korean Ver.) DBSK: Keep Your Head Down, Catch Me, I Don't Know (Japanese/Korean Ver.) SHINee: Replay, Amigo, Ring Ding Dong, Lucifer, Hello, Sherlock Super Junior: TWINS, Miracle, She's Gone, It's You, Love Disease 2NE1: I Don't Care, Go Away, You & I (Park Bom's solo), Ugly, Lonely
Here is my kpop list from youtube, I hope you'll find something to your taste- many different artists are on it.
Also highly recommended - all FT island ;) My favorite band - the list - now when I checked half of the songs are in Japanese, but well they are a Korean band ;)

The good way to start is to watch EYK's Kpop Music Mondays - they got me addicted by making kpop more approachable for me.
Everyone has already given some really good suggestions, I don't know much about K-Pop but I know what I like, and from trying to introduce the land of K-Pop to some friends, have found what most of them like as well.. Here is my playlist for Korean and Japanese(very little) music,
hmmmm
Same here I have no idea how to get into kpop more! I listen to 2ne1 and Bigbang, superjunior and so on but I'm kinda lost hahaha
Beast touch teentop boyfriend infinite z:ea u-kiss 2am MBLAQ 2pm Shinee cnblue super junior ft island exo -k bigbang all these are pretty good and worth checking out!! XD b1a4 nu'est 100%
B.a.P - Stop it;No Mercy;What the Hell Teen Top - To You;Crazy Infinite - Paradise;Only Tears FT. Island - I wish; love love love; hello hello Fat Cat - My Love HyunA - Bubble Pop Ailee - Heaven;Storm B1A4 - Hey Girl; Baby I'm Sorry Beast - Bad Girl;Beautiful Night Junhyung (from Beast) - Living without you Bob4 - Mystery Girl F(x) - Nu Abo Nu;Danger; Beautiful Stranger. These are just a few. ^-^ if you want a whole reaaaaally long list with good songs just mail me. :P
For good start I recommend: B1A4, Block B, Infinite, Boyfriend, B.A.P, MBLAQ, U-Kiss And girl groups: Kara, Girl's Day, Spica, Rania, Chi Chi If anybody wants more/something more specific, feel free to message me ^^ I'm into kpop since 2009 ^^
Here's a ranking for South Korean girl groups which was done this year by a mobile service provider:



Whether it's spot on one has to decide for herself/himself but it's quite a good roundup of all relevant groups.

(Top Tier Groups)
1. Girls' Generation (SNSD)
2. 2NE1
3. T-ara
4. Wonder Girls
5. KARA

(Mid Tier)
6. f(x)
7. miss A
8. SISTAR
9. Brown Eyed Girls
10. 4minute
11. After School
12. SECRET

(Bottom Tier)
13. A Pink
14. Girl's Day
15. Dal★Shabet
16. Rainbow
DBSK was my first K-Band in which I felt in love with :) I really recommend it to you!
Sung Joon- Jaywalking, Wake Up, Today J-Min- Stand Up Kim Hyun Joong- Please, Breakdown, Stupid, U BEAST- I like you best G-DRAGON - Crayon
try beast also known as B2st they are really good
I would listen to SNSD first... Gee and Genie are good songs to start with SHINee: Replay (currently my ringtone even though it's like 4 years old haha), Hello, and Lucifer. Super Junior: Memories is a cute ballad song... CNBLUE: Hey You is awesome if you like Maroon 5 MBLAQ: It's War, Run, and Mona Lisa are good... Rust is one of my favorite ballads from them Miss A: Touch, I Don't Need a Man SISTAR: Loving U, Alone Older songs I like are KISS' Because I'm a Girl, SES: Soul II Soul, and Rain's I Do