Movement mods, this is how far you need to move to be harder to hit.
3 hexes = +1
5 hexes = +2
7 hexes = +3
10 hexes = +4

Modifiers based on your movement. If you run, you take a +2 penalty to shooting.
Jumping = +3
Running = +2
Walking = +1
Not moving at all, not even changing facing = +0

Modifiers based on range
Short range = +0
Medium range = +2
Long range = +4

Pilot skill is [Gunnery/Piloting] So a 3/4 is Gunnery 3, Piloting 4, lower is better. When you calculate your to-hit roll, you add your gunnery, your movement modifier, their movement modifier, cover, and range. e.g. My 3/4 pilot ran, shot a target in the open at medium range, and that opponent ran 5 hexes and is in the open. The number I have to roll is: +3 [Gunnery], +2 [I ran], +2 [Medium Range], +0 [Target has no cover], +2 [Target moved 5 hexes]; total: 9+ to-hit using 2d6.

These are the basics. You *need* to memorize this stuff, the more advanced tactics you can use expand on these basic principles and are things you'll figure out naturally as you play.


An important notice:
One of the things you should never do is run your mech 2 hexes for a movement modifier of +0. Let us say you ran for +0, and your opponent ran for +1, and you are both 4 gunnery pilots at short range.

+4 gunnery, +2 running, +0 target mod = 6+ to-hit
vs
+4 gunnery, +2 running, +1 target mod = 7+ to-hit

Which means he has a ~72% chance to hit you and you have a ~58% chance to hit him. The majority of the time if you could have run for a +0 you could also have walked for a +0 or just stood still. Lets compare that:

+4 gunnery, +1 walking, +1 target mod = 6+ to-hit [Now you're shooting on equal terms with your opponent]
+4 gunnery, +0 didn't move, +1 target mod = 5+ to-hit [Now you're shooting better than he is]

Never. Ever. Run for a +0. Ever. (there are exceptions, but for the purposes of this guide, never is a good idea.) There is almost /always/ another move you could have made where you walk for +1 or stand still for +0 instead. Even simply standing still and taking a beating is preferable to running for +0.


Moving on from this, the next thing you want to look at is Initiative.
A string of good initiative rolls can pretty much take you from a guaranteed loss, to a win.

The ultimate position in mech vs mech combat is behind the enemy mech, preferably in a spot that he can't shoot you at all. Every move you make, you should be considering this. "Can I get behind him? If I do, can I kill him in one turn? If I don't kill him this turn, am I in trouble next turn? Will I be stuck in a killzone if I go for that backshot? Can I maneuver into cover after shooting him, or go for another backshot if I win initiative?" etc. etc. Backshots are very important because almost every mech design out there has less rear armor than front armor.


Okay, so you've won initiative, now what?
Well, the first thing you do is move your "useless" units first. This applies even if you lose initiative, but is even more important when you win. If you have a good backstabbing mech near the enemy, don't move the backstabber first. Slow 3/5 mech? Move it first, it's not going anywhere. Legged mech? Move it first, it's not going anywhere. Prone and unconscious? Move it first, it's not going anywhere. Sniper in partial cover at 15 hexes? Move him first, he's not going anywhere. [See the pattern here?]

If you've got a backstabber that moves 15 hexes at a time, move him LAST because he *is* going somewhere. [Namely, towards someone's back.] What you need to be careful of, is that you don't move your backstabbers until you've moved ALL of your "useless" [for the purposes of backstabbing] mechs first. That means if he moves the mech you want to backstab, you *do not* immediately move your backstabber to hit him. Good players will use the rear armor of their mechs as bait so they can rip apart your backstabber at short range with their other units.

When you move last, it means all his other supporting units will have moved, and you can better estimate your chances of success and survival, without worrying about a unit you never even saw, popping up out of nowhere and killing you.


Okay, so you've lost initiative, now what?
Stop, and think about the situation. Consider how you would want to move when you win initiative - don't let your opponent do those things. You still want to move the slow and useless units first because their movement is meaningless, they aren't going anywhere. That will free you up a little to react with your units. When he moves a light backstabber behind the camping mech that you just stood still, you can decide if you want to move your reactionary units in to deal with it or not.

By losing initiative you are placed on a more conservative footing, and you must be careful how you engage and what you engage, as your opponent will be able to choose the best range brackets and covered positions for his units. Sometimes it can be best simply to disengage and fade into cover or out of LOS. This can work very well in double blind play if you have active probes, as you will see him, but he will not see you, which allows you to judge when and where to strike, even if you've lost init.


What targets should I prioritize?
The weakest ones first, and concentrate on them. Don't spread your damage over everything - a dead enemy mech is better than 3 moderately damaged but fully operational ones, because you reduce the incoming firepower. Priority targets should be mechs with XL Engines, low speed, low armor and lots of ammunition. The worst targets are "zombies" which have standard fusion engines and (usually) energy weapons only.

Mechs are killed when they take 3 engine crits or the pilot dies, but you can make a mech near useless by taking out a leg or the gyro. When this happens, it is usually better to start focusing on another mech than to keep pounding on the crippled one.

Something to keep in mind as well, is firing order. It is important to hit with the big weapons like the AC/20 or ERPPC first which will punch a hole in a section, followed up by scattershot weapons like LRM's, SRM's and LBX Cluster. The reason for this is because you want to hit the internal structure of the enemy, which will give you a crit chance and could result in ammo explosions and disabled weapons in the enemy unit. A weapon like LBX Cluster deals damage in 1 point clusters, which allows you to sandblast a mech with an open torso as each pellet rolls for a location - with an LBX20, it's very likely that you hit almost every location on a mech at least once.


Fight the Powah
Battletech is about 50% player skill, 20% army composition (could be considered player skill), 20% terrain, and 10% luck. Sometimes that 10% luck dicks you over, and sometimes it gives you a win you didn't deserve.

When it comes to a loss, the best thing you can do is blame yourself for it - Not the RNG, not your opponent's cheesy army, not the terrain - Yourself. When you blame everything else, you tacitly imply that you are not making a mistake. This is the wrong stance to take - accept your mistakes, and learn from them. Try to figure out how you could have won that battle. Maybe you had the wrong type of army, maybe you made the wrong move somewhere. Every result that happens in the game happens directly because of what you did, how you moved that unit, what your opponent's response was.

The best thing to do when you get screwed over by the RNG, even though it can be hard, is to just grin and bear it. Keep playing, the RNG often swings both ways during a game, he headshot you, you headshot him later.