der Besuch
visit
The act of going to see a person or place for a certain amount of time.
Wir planen am Wochenende einen Besuch bei meinen Eltern.
We're planning a visit to my parents this weekend.

visit / visitor
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visit
The act of going to see a person or place for a certain amount of time.
Wir planen am Wochenende einen Besuch bei meinen Eltern.
We're planning a visit to my parents this weekend.

'Der Besuch' (the visit/visitor) is the noun related to the verb 'besuchen' (to visit). It describes the act of visiting. If you know the verb, you can easily derive the meaning of the noun.
Wir besuchen morgen meine Tante. Der Besuch wird nicht lange dauern.
We're visiting my aunt tomorrow. The visit won't take long.
The verb often tells you whether the action or the person is meant. 'Besuch haben' (to have visitors/guests) or 'Besuch bekommen' (to get visitors) usually refers to the person or people. 'Einen Besuch machen' (to make a visit) or 'ein Besuch bei jemandem' (a visit to someone) refers to the action.
Wir haben heute Abend Besuch.
We have guests this evening.
'Besuch' (visit/visitor) is often used in fixed expressions with verbs. Common ones are 'zu Besuch sein/kommen' (to be visiting/to come for a visit), 'Besuch bekommen/haben' (to get visitors/to have visitors), and the somewhat more formal expression 'einen Besuch abstatten' (to pay a visit).
Meine Cousine aus Hamburg ist für eine Woche zu Besuch.
My cousin from Hamburg is visiting for a week.
When you visit a person, you use the preposition 'bei', e.g. 'ein Besuch bei Freunden' (a visit to friends). When you visit a place or an event, you usually use 'in' or 'von', e.g. 'der Besuch im Museum' (the visit to the museum).
Der Besuch bei meiner Großmutter war sehr schön.
The visit to my grandmother was very nice.
guest
'Besuch' and 'Gast' can both refer to people who come to someone. The difference is in the perspective. 'Besuch' can mean the action, that is, someone coming, or the visitors as a group. 'Gast' means one person or several people who are invited, hosted, or served in a hotel or restaurant. People often say 'Wir bekommen Besuch' (We're having visitors / guests) when someone is coming to their home. 'Gast' sounds more natural when the person's role is important: they are invited, received, or using a service.

Am Wochenende bekommen wir Besuch von meiner Tante.
This weekend, my aunt is coming to visit us.
Der Gast im Restaurant fragte freundlich nach der Rechnung.
The guest in the restaurant politely asked for the bill.