Please help, I'm not getting this, 听来我不懂! Could you please use examples in your answer?
Obviously, this is a tricky one.
I know these three phrases have some same words and looks no differences for foreigner, but they are very different! If I give you one example for each phrase, you still will get confused when you meet a different one, so I'm gonna show you how to fishing instead of just give you a fish, in another word, master those three 'bastards'.
看来: mean looks like or seems. This phase usually stand for an quick and dramatically attitude change, like it or not doesn't matter. Example: "I told you so (我告诉过你)." the other person most likely say "looks like you are right. (看来你是对的)" despite that he/she didn't want to admit it. Or he/she admit it after learned by his/her own experience, example: "the lung exam show there are cancer cells in there, looks like I should quit smoking. (肺部检查显示那里有癌细胞，看起来我应该戒烟)"
看出来: mean figure out, get some results. I give you some thing, some entity, some person, some question, some being, some creature, some machine, you look closely, study, research, do stuff, and I come back, ask you "你看出来什么门道儿了吗？(Did you figure out something yet?)", it means I want get some results, some answers from you, those information go in and through your brain, you process them, and you need to produce something, give some output.
看起来, mean (it/he/she/thing) looks like or seems. When use this phrase, it means whatever the subject or object is, it usually not taking too much effort, or no need to get a closer look, or a deep digging, the answer is easily observed from the appearance of object or direct message from the subject/matter. Example: "It looks like our suspect's get away car just get away without him." "看起来我们嫌疑犯的逃脱车没带他就跑了。" and there is one more, in the US movie/television show, when a cheating scene get caught, the character usually say "it(thing) is not what it looks like." you shouldn't translate or express in Chinese with "这(件事)并不是看起来的那样。", because this is better "这(件事)并不是看上去的那样。", there you go, you just learn another one.
And, by the way, you really should register a stackexchange account!
看来：It seems; It is more about making a conclusion based on understanding or making assumptions about feelings.
Examples: 看来，你喜欢她(It seems that you like her.）；看来，你讨厌她(It seems that you hate her.)；看来，她不会来了(It seems that she is not coming.)；看来，你错了(It seems that you are wrong.)；看来，你对了(It seems that you are right.).
看起来：It looks like; It is more about conclusions based on observations of facts.
Examples:看起来，天快黑了（Looks like it is about to get dark）；看起来，她喝多了(Looks like she is drank)；看起来，没事了(Looks like everything is okay now)；不像看起来那么简单(It does not look like to be so simple)；我有黑圆圈了，看起来我应该每天早点睡觉(I have dark circles under my eyes, looks like I should go to bed early every day)。
看出来:Have you figured it out? Have you noticed?
Examples: 你看出来他喜欢她了吗？（Have you noticed that he likes her?）她看出来情况不对 （He noticed that something was wrong.）
看得出来：I can tell; we can tell; He can tell; *** can tell.
Examples: 看得出来，你喜欢她；（We can tell that you like her）; 看得出来，你跟不不喜欢你的工作 （We can tell that you do not like your job at all.）