In the past few months I've had the opportunity to chat with a lot of different startups in a lot of different stages, and I've noticed something common to many of them: they spend little to no time doing conversion optimization, and, as a result, their main conversion flows don't perform nearly as well as they should.
To them this is an acceptable compromise, instead of improving conversion optimization they are focusing their limited resources on building and improving their product; they'll focus on conversion optimization later. This line of thinking is wrong.
Conversion optimization is part of building a product people want
A website that converts poorly is equivalent to saying a lot of people visited the website and didn't want it. It doesn't matter how great the underlying product is, if it isn't expressed to potential customers in a convincing and engaging way, they won't use it.
Basic conversion optimization is simple
In my experience, simple tweaks, such as changing or re-ordering the questions in a conversion flow, make a much larger difference than time-consuming exercises, such as full page redesigns or fancy frontend UIs. Of course figuring out what tweaks to make can be difficult, but often it isn't. It is possible to make large improvements in conversion rates without huge amounts of effort. Conversion optimization is also an easily quantifiable activity, so you can measure whether it is a good time investment or not.
Conversion optimization is a rising tide
Conversion optimization is a rising tide that lifts all boats. Whatever organic traffic you get becomes more valuable automatically. Your referral marketing becomes more potent. And very importantly, improved conversion rates can enable you to unlock new paid marketing channels.
For example, if a particular marketing channels costs you $6 for a conversion, and the value of each conversion is $5, then that is a marketing channel you can't use profitably. But if you can reduce the cost per conversion to $5 or less, then you unlock that channel along with the scale and revenue it can generate. Marketing channels are binary, either you can use them profitably or you can't. Conversion optimization is often the easiest way to bridge this gap.
So, how do you improve your conversion rates?
This post isn't going to be an expansive guide to conversion optimization, but I'll include some basic ideas and examples to get you started. These ideas will also strive to be the simplest changes that can have the biggest impact. 
Conversion is about earning confidence and spending it wisely
There is an internal gauge inside potential customers measuring how much confidence they have in your website, which dictates how they are going to interact with it. Are they going to buy your product? Are they going to create an account? Are they going to give you their email address? Only if their confidence level is high enough.
The confidence level is affected by much more than on-page elements. For example, if a friend gives me a glowing recommendation of a new website, I'll have much more confidence by default than if I happened upon that same website via a random Facebook ad. But external considerations like this are hard to measure, whereas changes made to on-page elements can easily be iterated and measured. So all the following ideas are based on tweaking the on-page elements to increase conversion rates:
1. Put the conversion flow front and center
A common mistake is to make a splash page trying to convince people to fill out a form, where the call to action on the splash page is a button leading to the form. When a potential customer visits your website for the first time, their confidence level is low and they are willing to abandon your website quickly. If navigating or understanding your website is too difficult, they'll leave.
Put the beginning of the conversion flow right there on the main page, above the fold. The customer has already shown intent just by visiting you website, don't require them to click again or scroll around to get into the conversion flow.
2. Put simple and relevant questions first
Abandonment will always be highest at the beginning of your conversion flow because confidence is the lowest. So the start of your conversion flow is the most delicate part, and a part where experimentation is key to figure out exactly what to ask.
As a rough guideline, the first questions should all be simple to understand, easy to answer, and relevant to your product. Don't ask too many questions or any complicated questions. If it takes more than a few seconds to answer the first batch of questions, then you are either asking too many questions or the questions are too difficult. This isn't to say you can't eventually ask many questions or difficult questions, just don't ask them initially.
3. Your conversion flow should sell itself
As the person goes through your conversion flow, they should be building confidence in your website. If it isn't obvious to a potential customer why they are answering a question, you shouldn't be asking it or you should explain to them why it is important. Every relevant question earns you confidence, but every irrelevant question loses confidence and risks abandonment. Don't ask for their name if you don't need their name. Don't ask for a password if they don't need a password. If you do need a password, don't ask for it twice. Less is more.
4. Ask for personal information last
This is where you are spending all that confidence you earned. Potential customers will always be cautious about giving away their full name, email address or credit card information. You don't want to ask for these things until their confidence in your website is at the highest, which will be the end of your conversion flow. Additionally, you should ask for personal information on its own separate page at the end of the flow, otherwise the mere presence of these questions might deter potential customers from answering previous questions.
By far the most common mistake I see in conversion flows is to put an email/password sign up form as a gatekeeper before even getting to the conversion flow. This is a horrible mistake, as this is asking for personal information before asking any relevant, confidence building questions. You are trying to spend confidence that you haven't earned, and your abandonment is going to be much higher than it should be.
Real World Examples
All these examples are from the same vertical, online dating, because they can essentially be compared directly. My comparisons and ratings aren't scientific, but if you look at the various websites you should get a good idea of what a great conversion flow looks like and hopefully get some ideas for your own website.
1: Don't have blind faith that these ideas are going to work, all websites are different. You should be A/B testing all your tweaks and iterations, and please test them intelligently.