Newton's Laws:
1) Law of inertia: bodies in motion remain in motion in a straight line at constant speed if no forces act on them. This is the basic law that says what things do when left alone, and notice it does not say what their motion will be unless you know how it started out. This ushers in the crucial role of initial conditions in predicting motion.

2) Law of acceleration: A = F/m, where A is acceleration (and is a vector), F is net or total force (and is also a vector, pointing in the same direction as A), and m is the total mass (also called inertia) of the system. This is the basic law that says how objects respond when something is being done to them, and that something is a net force. Notice that this law means we need to understand changes in motion, not motion itself-- motion is not a search for some kind of "natural" behavior for an object, it is merely a study of how the motion is being changed.

3) Law of action/reaction: Forces come in action/reaction pairs, which are equal in magnitude and opposite in direction, act on two different bodies, are the same type of force, and show that forces represent a kind of relationship between two things. There is never one force without the other, so a closed system with no outside influences or outside bodies to act on it will always have a net force and a net acceleration of zero. Parts of the system, however, can have net forces and accelerations, so action/reaction pairs do not cancel out when analyzing these individual objects. Also, not every equal and opposite pair of forces is an action/reaction pair, they must have the above attributes to qualify. In particular, the reaction is always present whenever there is the action, there is no way to imagine a different scenario that could have one force without the other.

Types of forces:
Gravity: F = mg at the surface of the Earth.
Normal force: acts perpendicular to a surface, and is whatever is necessary to keep the object from entering the surface, no more and no less.
Friction: acts parallel to a surface, in a direction required to reduce or prevent slippage. Comes in two flavors, static friction if there is not yet any slippage (or if you have rolling), and kinetic friction if there is slippage. Kinetic friction has a formula, it is the normal force times the coefficient of kinetic friction. Static friction does not have a formula, it is whatever it needs to be to prevent slippage, but it does have a formula for the maximum strength it can be before it reverts to kinetic friction and slippage occurs. That formula also looks like the normal force times a coefficient, but the coefficient of static friction is a little larger than its kinetic cousin.
Tension: acts along the direction of a rope or chain, pointing outward from each end of that rope. It is like the normal force in the sense that it is whatever it needs to be to keep the rope from stretching, but it appears in equal magnitude at both ends of a massless rope, to insure there is no net force along the rope. If the rope bends, the tension at both ends do not need to point in opposite directions, they need to point along the rope at the end. If the rope is draped over a pulley, one can think of the rope as though it had two new ends at each side of the pulley, and the tension is the same at those ends as everywhere else in the rope. Indeed, you can arbitrarily break a rope up in your mind, giving it as many ends as you want, but it will always have the same tension throughout if there is no friction and the rope is massless.

An important thing for learning physics is to try problems yourself. Here I will write a few sample problems, similar to what was done in lecture, in a format that you might see them on a test. Bear in mind that some tests will give the quantities in the form of letters, which is flexible and conceptual, while others will give you numbers with units, which is specific and concreted but not flexible and not conceptual. So if you are given numbers, you should first replace them with letters, then manipulate the letters by whatever logical reasoning process is required to solve the problem, and then at the very end, plug in the numbers. This is superior to using numbers all along for a variety of reasons, the most important being that you can always look down at your equations and see what they are telling you about the logic you are using (taking limits of the quantities as they go to zero, for example). So all the questions I will give you will use letters and not numbers, but if you get numbers, solve the letters and plug in the numbers in the final step as necessary.

Sample problem 1: Two blocks of mass m1 and m2 are on a frictionless level surface, connected by a massless rope. The block with mass m1 is subjected to a horizontal force F, and the whole system accelerates along the direction of F with an acceleration you can calculate. Find an expression for the tension T in the massless string.

Sample problem 2: Take the same situation as problem 1, except now give the string a mass m3. Now the force from the string on m1 can be called T1, and the force on m2 can be called T2. Find T1 and T2, and notice that they are not equal. Also find an expression for the acceleration of the system.

Sample problem 3: A plane is inclined at an angle theta from the horizontal, and a block on the plane is held stationary by the static friction force. The block has mass m. Find the static friction force as a function of theta. Now find the coefficient of static friction if the block breaks free of static friction at a given critical angle, call it theta-star. Thus you are getting the coefficient of static friction as a function of the observed critical angle theta-star. Show that this critical angle does not depend on m. Now find the frictional force (which will be kinetic friction) if you are given the coefficient of kinetic friction, and you are told that the angle theta is greater than the critical angle theta-star. Sketch a simple plot of the frictional force as a function of theta throughout all parts of this problem, i.e., in both static and kinetic regimes.

When you can successfully complete all three of those problems, you understand tension and friction admirably. Here are the solutions:
1) The acceleration is F/(m1+m2). Thus the force on the rear block obeys T = m2*a = F*m2/(m1+m2).
2) The acceleration is now F/(m1+m2+m3), looking at the total system. Thus the force on the rear mass obeys T2 = m2*a = F*m2/(m1+m2+m3). The force on the string obeys T1-T2 = m3*a = F*m3/(m1+m2+m3).
3) The static friction balances the component of gravity along the plane, so that's mg*sin(theta). At theta-star, the maximum force is mu_s times the normal force, so we then have mg*sin(theta-star) = mu_s*mg*cos(theta-star), which solves for mu_s = tan(theta-star). Thus the frictional force rises with theta until theta hits theta-star, and then it drops down to the kinetic friction value, which means a sudden drop by the ratio of mu_k to mu_s as theta goes imperceptibly above theta-star.