Lie v. i. (lay, lain; pres. p. lying) 1. (of persons or animals) To have one’s body in a more or less horizontal position; to be or put oneself flat on a horizontal surface or in a resting position; to be at rest, e.g. to ~ still; to ~: on one’s back; don’t ~ in bed all morning; 2. (of things) To be resting flat on smth., to be at rest, usually more or less horizontally, e.g. the book lay open on the table; how long has your bicycle been lying out on the wet grass? 3. To be kept, remain, in a certain state or position, e.g. money lying idle in the bank; towns lying in ruins; to ~ helpless; the snow lay thick on the ground; the fields lay thickly covered with snow. 4. To be spread out to view; extend; stretch; to be situated, e.g. the valley lay before us; the fleet lay off the headland; the road ~ s straight across the prairie; ships lying at anchor; life ~s in front of you. 5. (of abstract things) To be, exist, be in a certain position or manner, e.g. the trouble ~s in the engine; he knows where his interest ~s; his motives ~ hidden; it~s with you to decide this question; the choice ~s between the two; the remedy ~s within yourself.
Lay v. t. (laid, laid) 1. To put on a surface; to put down, e.g. to ~ one’s hand on smb.’s arm. 2. To put down in a certain position; to place, e.g. to ~ bricks; to ~ the foundation; to ~ linoleum. 3. (of birds and insects) To produce and deposit, e.g. Hens ~ eggs. 4. (with various objects) To put or keep down; to cause to be in a certain position; to suppress, e.g. to sprinkle water on the road to ~ the dust; to ~ crops; to ~ one’s doubts. 5. (pass.) To set (a story, etc.) in time or place; e.g. the scene of the story is laid in Coventry. 6. To place or arrange (ready for use, etc.), e.g. to ~ the cloth; to ~ a fire. 7. To set a trap, etc., e.g. to ~ a snare for smb. 8. To attribute, ascribe, charge, e.g. the murder was laid to Jones; to ~ the blame for smth. on smb.; to ~ an accusation against smb.; to ~ smth. to smb.’s door.
To lie (лежать) and to lay (класть, положить) are very frequently confused because of the similarity, and partial coincidence in form and proximity in meaning. The importance of these two verbs can hardly be overestimated. Both occur very frequently in Modern English, are highly polysemantic, enter a great number of phrases and can be used with many different prepositions and postpositions. Try and memorize as many of the examples suggested as possiblie, and avoid confusing them.