The chart below lists the dictionary forms of verbs meaning be, get, and put in these three positions. The verb to the left of the slash is Imperfective, e.g. вставђть/встђть = Imperfective/Perfective, resp.
  standing lying sitting
be стоїть лежђть сидљть
get вставђть/встђть ложќться/лљчь садќться/сљсть
put стђвить/постђвить клђсть/положќть сажђть/посадќть
1. be-verbs
Unlike English, сидљть is never said about objects; only people and animals can do that. Also unlike English, there is a fairly strict distinction between objects that can only 'stand' and those that can only 'lie.' As a rule of thumb, use стоїть with any object that has a natural base (such as the bottom surface of a drinking glass, the bottom rim of a dinner plate, or the legs of a chair). Use лежђть with everything else. (This is also described in Standing vs. Laying/Lying).
When used with objects, the verbs стоїть and лежђть often correspond to English 'be':
  Стакђн стоќт на столљ. The glass is (standing) on the table.  
  Рџчка лежќт на столљ. The pen is (lying) on the table.  
2. get-verbs
The verb вставђть/встђть means 'get up from a sitting or lying position'. It is also used to mean 'get up' in the sense of 'get out of bed, rise'.
  Ї обІчно встає в сљмь. I usually get up at seven.  
The verb ложќться/лљчь 'lie down' can be used in the sense of 'go to bed'.
  Ї обІчно ложџсь в дљсять. I usually go to bed at ten.  
3. put-verbs completeness.
The verbs сажђть/посадќть mean 'seat', as in seating people at a table. You won't need this verb very much — we put it here for the sake of completeness.
4. get-verbs & put-verbs: кудђ or гдљ?
These involve motion, so the natural thing to do is think of these as кудђ situations and use the Accusative with the appropriate prepositions:
Location (be): Ћн сидљл за столћм (на стџле). He was sitting at the table (on the chair).
Motion (get): Ћн сљл за стћл (на стџл). He sat down at the table (on the chair).
Motion (put): Ћн положќл егћ на стћл (в шкђф). He put it on the table (in the cupboard).
However, sometimes some of these actions can also be seen in terms of the location where you do that. E.g. 'lie down in the study,' 'sit somewhere around here.' This is mostly possible when talking about rooms and other large areas, not chairs or couches.
  Ћн лёг в гостќной (Prep.). He lied down in the living room.
  Ћн сљл тђм, гдљ бІло теплћ. He sat down where where it was warm.
  Гдљ (or: кудђ) мћжно сљсть? Where can I sit?