I would like…

… a cut (需要剪掉一定量的头发，接着你可以说具体要剪多少)

… a trim (只是修一修，整体发型不要变。)

… make my hair thinner（打薄）

… a wash and cut. (先洗再剪，洗发会增加额外费用)

… a wash, cut, and dry (or style). (洗剪吹全套)

… to get a perm. (烫发)

… to have my hair straightened. (拉直)

… to have my hair dyed or coloured. (染发)

几个方位词：

in the back 后面

in the front 前面

on the sides 两边

on the top 头顶

综合运用：

理发师: How would you like your haircut, sir？ 您想怎么剪？

客人: Just a trim, and cut the sides fairly short, but not so much at the back. 稍微修一下。两边多剪短些，后面不要剪太多。

理发师: Nothing off the top? 头顶不剪吗？

客人: Well, a little off the top. 哦，上面稍微剪一点。

理发师: How about the front? 前面呢？

客人: Leave the front as it is. 前面不要剪。

其他词汇

parting line 头发分界线

setting lotion 烫发药水

highlight 挑染

shampoo 洗发水

hair conditioner 护发素

styling gel 发胶

fringes 刘海

layers 层次

split ends 分叉的发尾

dandruff 头皮屑