I have two tables Activity and Action. One or more actions can be performed for an activity. And the relationships between Activity and Action is given in a third table call
SELECT ActivityText AS Activity, ActionText AS ApplicableAction
  FROM Activity 
  JOIN ActivityAction on Activity.ActivityId = ActivityAction.ActivityID
  JOIN Action on Action.ActionId = ActivityAction.ActionID
You have IDs in Action table and when you join table ActivityAction on ActivityId key then you are able to join activity table
SELECT ActivityText, ActionText
FROM Activity
JOIN ActivityAction ON Activity.ActivityId = ActivityAction.ActivityId
JOIN Action ON ActivityAction.ActionId = Action.ActionId
WHERE Activity.ActivityId = 1;
                                                                        This should do the trick
SELECT Activity.ActivityText as Activity, Action.ActionText as ApplicableAction
FROM ActivityAction
    INNER JOIN Activity
        ON ActivityAction.ActivityId = Activity.ActivityId
    INNER JOIN Action 
        ON ActivityAction.ActionId = Action.ActionId
You should read up on JOINS in databases. Here is a good starting point:
http://en.wikipedia.org/wiki/Join_%28SQL%29
Basically what we have here is a many to many relationship between Activity and Action which is resolved by two one-to-many relationships using the a join table called ActivityAction.
To get the required data back, we are joining ActivityAction to each one of the tables using the appropriate PK and FK columns and then choosing the string columns in the SELECT