GRE requires a wider skill-set than TOEFL. Before starting the preparations for the exams, you should book the dates. A three-month preparation is reasonable for GRE. For TOEFL, the preparation time varies, depending on how much time you’ve spent outside of the college textbooks with English.
Take GRE before TOEFL, because in GRE you’d need to learn a large number of words. This large vocabulary will help you read, listen, speak and write better in TOEFL.

For GRE

For the Verbal Section

Step 1: Buy a book.

ETS’s GRE is a wonderful starting point. Barron’s GRE was my reference.

Step 2: Familiarize with the pattern of questions.

Jump into doing sample papers, given in the book. GRE is a 4 hour exam, so don’t time your first attempts. Look at the multiple question sets to get a sense of the pattern.

Step 3: Do the lessons in the book.

There will be an assortment of some standard tips on how to attempt certain types of questions. Skim these.

Step 4: Signup for an online course.

This might look like a bad investment to start with. But, an online course of $100 will save you from doing badly in your GRE first attempt. Most people don’t signup, and then retake GRE (which costs $180!). If you know someone else who’s preparing for GRE, share the membership fee and the password. My website of choice is Magoosh Online Test Prep. It also has a free Android app, and thus everything gets complimented smoothly.

Step 5: Build your vocabulary and writing style.

This is crucial, and is not easy. Remembering the 4000 word meanings is very easy. But knowing where and how they are used, is not. The slow and thorough method is to read as much of literary fiction as possible. But you’d have to settle for reading newspaper. Not Times of India or even The Hindu. Accelerate your pace by reading The New York Times [has the best writers and newstories], The Guardian [has the best interface, and its Android app is gorgeous], The Atlantic, The New Yorker [if you’re feeling fancy]. I took the New York Times subscription. Without the subscription you get to read 10 articles. It costs $1 for the first three months. Cancel your subscription before three months (or keep it!). Reading high quality news pieces and articles is imperative because it prepares you for reading section of TOEFL, analytical writing of GRE and writing section of TOEFL. Read the opinion/analysis sections of various news websites to understand making your points precisely and professionally.

Step 6: Do all the exercises of the book and online course.

You paid for everything, so do every question of the book and online course.

Step 7 [concurrently with steps 5 and 6]: Answer one analytical writing question everyday.

When you take the GRE, the first hour goes in typing two essays. If this section goes badly, whole of your exam will. Look at the ETS’ example of best answers. The longer your essays are, the more mark it gets. But, you’ve 30 minutes for each of the questions, so learn to type while thinking and to type fast. To improve your writing use hemingwayapp.com to write. It improves the writing style, as it points out places where you’re using too many adverbs (which is a bad writing practice).

The ETS’s official website has a pool of topics, from which the questions will be asked! Take one topic everyday, and type it out!

The harder you work, the luckier you get.

For Quantitative Section

The questions are from basic math — algebra, geometry, trigonometry and some statistics. Take ETS’s official book and do its quantitative section. If you’re from a STEM discipline, this section is easy. But, it’s also dangerous because it’s easy. Making one mistake or leaving one question, can cost you 2 points.

For TOEFL

There’s a detailed version for TOEFL preparation is written in another story.

If you’ve worked on GRE’s verbal section well, you’re prepared for 50% of TOEFL. There are four sections in TOEFL. Buy a book, there’s usually a CD in it. Do the CD, and familiarize yourself with the overall exam. Once you know the pattern of the exam, watch NoteFull YouTube tutorials. For TOEFL, the most important thing is to avoid surprise. The speaking section of TOEFL is intimidating because, they give you 20 seconds to prepare, then ask you to speak for 60 seconds. The speaking section is more of an extempore session. So, you need to know each type of questions and have a strategy for each of these types of questions.
Listening section of TOEFL is easy, but is tiring since you have to take lots of notes. Always make notes in this section!
Reading section needs patience, but is otherwise exceptionally easy.
Writing section is easier than GRE, but there’s an integrated writing task which requires your listening skills too.
You’ve to take 10 full TOEFL sample exams to master it. Take the CD that comes with the book very seriously. I bought Baron’s TOEFL, and it had everything that’s needed.

Invest money in preparation, rather than taking these exams twice. After GRE and TOEFL, you’d be a better writer and reader.