The verb вести means to guide someone somewhere. It's a unidirectional verb that conjugates like this:

Unidirectional verbs have multiple interpretations. The first one is applicable when you spot someone going somewhere with someone else.

Unidirectional verbs in the present tense also have the meaning of ‘intent in the immediate future’:

In the past tense they focus on action in progress at a particular point of time:

There is a subset of verbs in Russian that in the US are sometimes taught as verb triplets instead of pairs. You can find a list of those verbs here, and a rough summary of how those verbs are used here. Among them is the multidirectional verb водить, which conjugates like this:

We can say that the verb means ‘to lead [someone somewhere by your own power].’ But to be honest we normally translate it as ‘to take’ in English. For instance...

Generally speaking the verb means that you are taking someone somewhere but not using a vehicle to get there. It can also be used if a vehicle is involved but the vehicle is not germane to the discussion. For instance, in the following sentence, the person speaking may live near the Kremlin Armory (so they can walk there with their guests), or they may just live somewhere within the city limits, but the fact that they will take the subway to get to the armory is simply not relevant to the story.

Водить can also mean to lead people around a place (random motion inside a prescribed area). In this meaning the preposition по + the dative case is used. For instance:

In the past tense the verb can also mean to take someone somewhere, and the implication is that they are no longer located at the location you mentioned.

The determinate verb for “to carry” in Russian is нести:

This is a determinate imperfective verb which means it is used to describe motion heading in a single direction. Although it means “to carry,” it is often best translated with variations on ‘take’ and ‘bring’:

The most generic verb for “to carry” in Russian is носить. Note the consonant mutation in the я form:

This is an indeterminate imperfective verb which means it can be used with the preposition по + dative to indicated carrying something here and there, all over the place:

Most indeterminate imperfective verbs can bear the meaning of “go there and back.” Носить is a bit odd in that it really isn't considered good style to use the verb that way. You will find it used conversationally, though, in that sense:

Notice that the translation of the last sentence doesn't contain the word “carry” in it. It is often the case that the Russian verbs of carrying (носить, нести, возить, везти, and the dozens of words derived from them) are best translate with “bring” or “take” in English.

Носить can also be used to take something to a particularly place on multiple occasions:

The most generic perfective verb for travelling by air in Russian is полететь “to fly”:

Perfective verbs like полететь have several different uses. The nature of the perfective verb is to put focus on the result of an action, so полететь can mean “to head off somewhere by air and actually arrive there.” Thus it can be used to describe a series of flights, each one complete:

The verb can also mean “to go and arrive” on a single trip; we see it in that meaning in a headline from Guy Laliberté's recent flight into space. (He is the founder of Cirque du Soleil).

One last use is a colloquial one. It can also mean “I'm gone,” just as побежал and пошёл can.