This is going to be the longest achievement in the game for you. To put it in perspective, using the same officer in the German E-100 line (tier-VI to tier-X), my highest ranking officer is rank 7, about three-quarters of the way to rank 8. This will take you many, many hours of fighting battles, but all is not lost! Here are some tips to maximize your XP earning.
[Major Edit! - Wargaming has finally come out and said how much crew experience you need to read Rank 10: 3,806,745. With that goal in mind, here's are some tips to complete the grind sooner rather than later.]
Step 1 - Skills: The first skill you want to learn is Mentor. It provides a 10% boost to experience. This applies to both crew XP and tank XP. The downside is you lose out on a different skill, because Mentor provides no in-match benefits. Choose other skills depending on your tank type, nationality, and play style. (See below for Skill/Perk recommendations.)
[Edit: The second skill you should earn (in order to maximize XP gains) is Brothers in Arms. This will provide an additional 5% boost to XP if you already have Mentor. These values (10% and 5%, respectively) are when you have 100% mastered the skill.]
Step 2 - Equipment: It's expensive, but buy the Improved Ventilation equipment for your tank. This can cost up to 600,000 silver, but it provides a 5% boost to skills. This is only useful if you learned Mentor, which is a skill that will get the 5% boost. If you don't have Mentor, do not buy Ventilation. It will not help you.
[Edit: Improved Ventilation ranges anywhere between 150,000 to 600,000 depending on what kind of tank you're driving and what tier.]
Step 3 - Consumables: Use your nation's food consumable. This is different for each nation, and it costs 20,000 silver if you switch currency types. Otherwise, it will cost 50 gold. This will give you another 10% boost to skills, and again, if you don't have Mentor, don't use food.
Step 4 - Tanks and Tiers: Use whichever kind of tank you're most comfortable with. I prefer heavy tanks, but it's ultimately up to you. You optimally want to pilot a tier-VIII premium or elite tank. This is because higher tiers give you more XP, and damaging more powerful tanks gives even more. You get more XP for fighting tier-X tanks, and as a tier-VIII, you'll get a modifier for being two tiers lower.
[Edit: Several users have mentioned they prefer tier-VII vehicles because the matches go faster. People in tier-X tanks can be extremely if not overly cautious, which can make matches drag on. Fighting tier-X tanks as a tier-VIII will give you more XP in a game, but you'll likely get in more games--and therefore more XP--by playing as a tier-VII vs. up to tier-IX.]
Premium and elite tanks give you a 25% crew XP boost, no matter what tier. You can switch back and forth between premium and elite tanks at no cost, so the more premium tanks you have, the more you can switch between them and capitalize on the x2 daily win bonus. Switching from one elite tank to another still costs money, and you will have to remaster the new tank even if you had previously mastered it. You cannot switch from one elite tank to a premium and then to another elite tank without paying this penalty.
[Edit: flodros pointed out that it doesn't need to be an elite tank to switch without paying silver/gold. You can freely switch between a non-premium tank to a premium tank regardless of elite status.]
Additionally, premium tanks also give battle XP modifiers that, unlike crew XP, are different for every tier. Here's a quick rundown:
Tier-II: 70% battle XP modifier
Tier-III: 60% battle XP modifier
Tier-IV: 50% battle XP modifier
Tier-V: 40% battle XP modifier
Tier-VI: 30% battle XP modifier
Tier-VII: 20% battle XP modifier
Tier-VIII: 10% battle XP modifier
Tier-X: 5% battle XP modifier
(Note 1: There are currently no tier-IX premium tanks. Tier-X premium tanks are PC-exclusives, but I listed them because they do exist and may come to console eventually.)
(Note 2: These modifiers come into play before the premium/elite modifier. For example, at tier-II you'll get a 70% boost for the XP you earn in battle, and then your crew will receive an additional 25% boost on top of that.)
[Edit: If you have not mastered your current tanks, your skills and perks are disabled until your crew is 100% trained in the new tank. Unlike with learning perks and skills, the XP you earn while mastering a new tank will still go toward ranking up your crew, but you will not have the benefits of Mentor and/or Brothers in Arms. Additionally, because your skills are disabled, using your nation's food consumables will not provide you any benefits, so don't equip any until you've mastered your tank.]
Step 5 - Premium Days: During premium time, you get another 50% boost to XP. You can either purchase it with real money or wait for an op that will give you free days of premium upon completion.
Step 6 - There is no step 6.
Step 7 - Ops: Always pick the ops that give bonuses to XP. This will go to both tank and crew XP, but modifiers from premium/elite tanks, skills, items, etc. will not apply to these rewards. Also be on the look-out for ops that give you premium time.
Step 8 - Other good skills: Regardless of tank type, you want to learn Brothers in Arms and Jack of all Trades as soon as possible. Having better crew members and reducing penalties for injured crew members is always nice. Pain Tolerance is okay but shouldn't be all that high on your list.
[Edit: Brothers in Arms will add a 5% boost to all your skills when fully mastered. If you have Mentor, it will increase the boost you receive from 10% to 15%.]
Preventative Maintenance is virtually a must-have for German and Japanese tanks. They're more prone to engine fires than any other nation. (Sarcastically: Thanks, RNG, as always, you're a big help.) Firefighting is less useful but also good.
Safe Storage is good for tanks with longer loading times, like heavy tanks and tank destroyers. Russian vehicles are more prone to damaged ammo racks than other nationalities. Artillery shouldn't worry too much, because if you're getting hit, your tank will blow up long before your ammo rack.
On that note, artillery should pick up Green Thumb, Muffled Shot, and Camouflage to remain hidden when stationary and firing. If you're a tank destroyer who prefers to snipe rather than charge in, these skills are good for you, too. Camouflage is the least useful of these three skills but still good to maximize your stealth and therefore longevity.
Light and medium tanks that like scouting should pick up Recon, Designated Target, Call for Vengeance, Off-Road Driving, Situational Awareness, and Silent Driving. That's more or less the order you should learn them in, but pick and choose whatever you like.
[Edit: If at any time you feel like switching skills, remember that you can pay 10 gold to switch a known skill for a different one. Again, thanks to flodros for the reminder.]
That's all the useful information I have to give, really. Keep at it, and hopefully Wargaming won't introduce an achievement for reaching rank 17. Good hunting, everyone.