Here's a simple mental picture to have of a how a burner on a stove heats up water in a pot (which is sitting on the burner). (In what follows, I will use the term "molecules" for both molecules and atoms.) Also, keep in mind that thermal conduction is different than electrical conduction. One (electrical conduction) concerns the flow of charge, so in this type of conduction, particles actually flow from one place to another. The other (thermal conduction) concerns the flow of heat (or energy), but no particles or molecules are flowing from place to place in this type of conduction.
1) When you turn on the stove, an electric current begins running through the burner (or through a resistor in the burner). Due to the resistance in the burner, the current causes the burner to heat up (just like any resistor warms up when you send current through it, due to collisions caused by the charges trying to move through the material in the resistor).
2) As the burner begins to warm up, the molecules in the burner are now vibrating more rapidly than they were initially. Sometimes these rapidly-vibrating molecules near the surface of the burner will collide with molecules on the bottom of the pot. These collisions transfer energy from the stove top (the burner) to the pot via thermal conduction.
3) As molecules on the bottom of the pot gain kinetic energy from the stove, these molecules in the pot begin colliding with other molecules in the pot, transferring heat throughout the pot, again via thermal conduction.
4) "Pot molecules" near the water on the inside of the pot can now begin transferring their kinetic energy to the water molecules via collisions (because all the molecules are vibrating). This causes water molecules at the bottom of the pot to start moving around more quickly, corresponding to an increase in the temperature of the water. Because the water molecules have much more freedom to move around than do the stove and pot molecules, the faster-moving water molecules at the bottom of the pot can now begin transferring their kinetic energy to the rest of the water via both conduction and convection.