A Good Engineer is a force multiplier, he:
*Denies access to vital parts of the map to the enemy team.
*Gets his teammates to the front lines quickly.
*Provides an extra source of vital healing.
*Allows other teammates to focus on what they do best.
A Bad Engineer:
*Takes up a spot on the team that could have been occupied by a simpler, more powerful class
*Is an inefficient use of metal, ammunition and spawn time.
*Requires other teammates to divert from their primary roles to assist/protect him.
*Provides an unnecessary ego boost for spies.
The Engineer class is more complicated than other 'point and shoot' classes, however it is still easy to quickly learn and play with the fundamental capabilities with the class. On the other hand, the engineer provides few hard counters to other classes and has large weaknesses in exchange for his unique abilities.
Those who claim that the engineer is easy are correct, to a point. The engineer is still easy to counter, and a countered engineer has an extraordinarily difficult time regaining momentum without the help of his team. Spies can be annoying; soldiers are a threat, and demomen even more so. An Ubercharge usually means the destruction of all of an engineer's front-line deployables, and with them, his effectiveness. Adjusting and compensating for these weaknesses takes quick thinking and a willingness to ignore the natural temptation to turtle as an engineer.
Without his deployables, the engineer is an unremarkable class, lacking speed, firepower, and in some cases, durability in comparison to the other classes. The shotgun and pistol are good, reliable weapons, as evidenced by the fact that they are crucial when used as backup weapons in the hands of a skilled soldier, heavy, pyro or scout. In the engineer's hands, it's even more important that one aims effectively with them and make every shot count, because without his sentry, he's badly outgunned by the other classes. The Wrench is a solid melee weapon with the standard delay and damage, but with the added crit benefit bestowed by the damage dealt by the sentry, usually resulting in more crits than any other weapon. The Wrench also has a significance psychological impact, humiliating when it kills and carrying a reputation for common crits.
The biggest challenge for the engineer is keeping up with the rapid pace of the game. The natural inclination is to build up on one spot, relocating only after the rest of the team has long since moved forward. This is just fine for defense, but on offense, it's unacceptable. Furthermore, it accentuates one of the biggest pitfalls the engineer faces.
Deployables represent a significant investment of time and metal to build and upgrade, and the natural impulse is to invest in an 'outpost' once your deployables have been upgraded. A sentry or dispenser that is behind the front-lines is not helping the team, and unless the engineer is defending a fixed location, he's just taking up a server slot when he maintains them.
It doesn't matter what level your dispenser or sentry is at, if the next control point has been captured, move up, detonate your old stuff and start again. Due to the time investment required to get your deployables back in working order, this means that you're going to have to devote as much time and effort as possible building your stuff rapidly. Furthermore, you should never, ever, sacrifice your life for your sentry ... it takes far longer to re-spawn then it does to rebuild. If it looks like you're going to loose your sentry, stop humping, get back and look for the next spot to build.
Locations to place your deployables are dependent on which map you're playing on and importantly, what your team is trying to achieve. Knowledge of the metal boxes on the map is vital. Dispensers build and give out metal too slowly to fuel an engineer that's moving up with his team on a push map. Build near metal boxes and utilize them, otherwise you'll lag behind and the benefit you provide will be limited.
As important as it is to effectively fight with your weapons, your skills are put to better use focusing on avoiding combat and building rapidly. A scout can easily outflank an engineer, and heavier classes will simply overpower an engineer, regardless of combat skill. If everything is built up and the team hasn't moved forward, by all means lend your firepower to the fight, just don't take unnecessary risks.
Spies are a pain, they destroy your equipment, have a buggy, broken, instant kill melee weapon, and their revolver outguns your shotgun at anything but point-blank range. Trying to out-repair a sap-happy spy is a lost cause, but don't get yourself killed unnecessarily. If you can avoid him flanking you, your wrench outdamages his knife, but a skilled spy will back off and switch to his revolver if you challenge him in melee combat and the flickstab doesn't work. If you get lucky, the spy will get far enough from your sentry to where you can repair it ... leading to a satisfying and poetic end to the confrontation, but it's not something you should bet on. As much as I personally hate spies, I'll admit that it's better to pull back, let your team deal with the pest, and rebuild as necessary, something you should be very good at from all that rebuilding on push-maps.
Looking back at what I've written here is amusing, especially considering that my actual play style doesn't actually follow most of the advice I've given. I'm far too aggressive. I recognize that I have much to improve upon, and it's easy to get carried away if you're not thinking ahead. But with that said, I don't nearly enjoy any other class nearly as much as I do the engineer. The class is simple to learn, difficult to master, a worthy challenge. The heavy is right when he says that a good engineer is a credit to the team.
NOTE: I started this thinking of making another video, but I realized that there isn't much here to take humor from, and making the video would require a lot of effort to provide information better presented in this form. I'll think of something to put in my next video ... eventually.