if you mean Goes upstairs or goes downstairs ,you can say :我要下楼 WO YAO XIA LOU 我要上楼 WO YAO SHANG LOU

i want to go up and i want to go down better to translate 我想上去。 and 我想下去。
pick me up one explanation is 去接我, but this phrase has also other meanings.
put me down 放我下去
phrase can have different meaning which can not be translated directly, so if u r confused, please turn to the help of dictionary. i believe that is also a good idea.

It should be "上去" and"下去".

我想上去。
我想下去.

Pick me up. 带上我。
Put me down 放下我。

我想上去
我想下去

Well, Rose, i wanna say that, in the direction sense, "up" can mean in or toward the north, namely 在/向北方 in Mandarin. For example, you can make such sentences as "I'm driving up to Beijing for the Olympics (我正驾车北上去北京看奥运会)" and "She lives up north (她住在北边)". Oppositely, "down" can mean in or toward the south, namely 在/向南方.
We have the saying of 北上南下 in Mandarin. So i think go up and go down can have the meaning of 北上 and 南下.
However, as suggested by the friends above, go up and go down have many meanings such as 上去 and下去. And i think its meaning of 北上 and 南下 is not used very often, so it can be confusing sometimes. What's more, a dictionary can always be a helpful friend! o(∩_∩)o...哈哈

north is up上,south is down下
high is up上, lower is down下
older is up上, younger is down 下

we say
我想去上。 wo3 xiang3 shang4 qu4
我想去下/我想下来。wo3 xiang3 xia4 qu4/wo3 xiang3 xia4 lai2

上 and 下 is verbs in chinese，the word itself represents the direction,while the vervs "go" has not direction property ,so we add "up" and "down" after the word.

i wanna go up/ 我想上去 or 我想上来
i wanna go down/ 我想下去 or 我想下来
pick me up/ 来接我(if you mean pick someone up by car for example);
pick me up/ 弄我上去(if you mean pick someone up to somewhere);
put me down/ 放我下去

我要上去
我要下去
把我带上
把我放下来

上 下