For your convenience I've separated the Youtube video optimization methods into two categories. The first category is called content and the second is called engagement. Content has to do with the things within your control when creating and uploading your videos to Youtube. Engagement has more to do with the response your videos are getting from your audience.
Content
1. Title.
Title's are what make people click on videos. You'll need to take some time to create a truly compelling title to each video and be sure to load your title with your most targeted keywords or phrase. Be careful not to over promise and under deliver. Ultimately your video will do well if your viewers approve and engage with it. If you make an overly aggressive title and fail to deliver on the content viewers are not likely to watch your video in it's entirety, and or leave comments and share it.
2. Description.
Your description should be thorough and at least a couple of paragraphs. Be sure to include your targeted keywords and phrases. Unlike Google Youtube doesn't do a good job with plurals and similar phrases. So if you want to rank well for a specific keyword or phrase you'll need to enter that exact phrase . For example if you're targeting "free websites" and "free website" you'll need to include both phrases in the description.
3. Tags
Be sure to include at least 10 tags. Make sure they're relevant to the video. If your video is all about something and you don't include the tag it won't get ranked on Youtube. It's not semantic like Google. Meaning you'll have to include every keyword and plural you want to get ranked for.
4. Transcription.
Youtube has a transcribe function. Youtube uses the transcription to help rank your video. Take the time to transcribe the video and upload the text file. It will also make your video closed caption and you'll rank better for the video. Include your targeted keywords and keyword phrases in the transcription. There is some evidence the transcription doesn't need to actually match the video. So sneaking a couple of extra keywords may be helpful.
5. Channel Authority.
Channel authority will be good if you're consistently creating quality videos. You can build channel authority by getting views and creating engagement with your audience. Having a link to your Youtube channel from your website is one helpful way to get more channel views and authority.
6. Delivery.
Ultimately great video content has a way of rising to the top. So whatever you do make a quality video that people want to watch and share. If you're creating a video about a subject be sure the title matches what's actually in the video. People hate to get "Rick Rolled".
Engagement
1. Views
This is a classic chicken and egg problem. To get views you need to get found - to get found you need views. You can start getting views by promoting your videos on other places across the web. Share your videos on your Twitter, Facebook, website, and wherever else you can think of. Once you start getting views it will help your video go popular on Youtube.
2. Inbound Links
Just like Google Youtube uses inbound links as part of their algorithm. Be sure to link to your videos from as many external websites as possible.
3. Social Shares
You need to share straight from Youtube to Twitter, Facebook, Google +, and other social media websites.
4. Embeds
Encourage people to embed your videos. Be sure to embed all your videos on your own website or blog.
5. Comments
Don't try to game the system try to inspire conversation. It helps to reply to posts to keep the conversation going. Try to encourage people to do video responses.
6. Likes and Favorites
Encourage people to like and favorite your video. This will rely heavily on your creating great videos.
By following these steps you're sure to get your videos to show up when people search Youtube and even Google. The more video views the more opportunity to convey information and drive traffic to your website.