Before I start I probably need to mention that search engine optimization (SEO) gets less and less important for most YouTube videos (despite tutorials as they usually rely on high traffic from other search engines). YouTube only takes textual information as a first start and ranks search results more and more according to retention rate and depending on how much they are watched from recommendations.
First you need to come up with some keywords that are relevant for your video. Lets assume you made a video about a fish explaining how to repair a toilet. Two primary keywords could be "howto" and "toilet". Two secondary keywords "fish" and "repair". Which and how many keywords you choose and if you group them in a tertiary or even lower group varies with video content and probably even season. Optimizing for YouTube search can be done in different manners:
- Good tags. Google Trends or the AdWords Keyword Tool can help to come up with examples. Just put your keywords in and choose other well searched terms that fit your content.
Note that if you choose any even if they are not relevant you will have a high viewer drop rate and thus a low retention rate which puts you down in the search results.
- Title. Put your primary keywords to the front of the title. To be also appealing for humans and not only search engines you should choose a catchy phrase. Attach a more describing phrase that contains your secondary keywords so that the title is e.g. "Insane Toilet Howto - Repair done by a fish "
- Description. Give a meaningful description. Stuffing blocks of keywords aka tag salad is forbidden by YouTube's TOS and all important search engines identify them anyways and probably even put a rank penalty on such search results.
Try to include the most important keywords in the first sentences and come up with synonyms in the following ones e.g. "Learn how to repair a toilet from a fish. This cute marine creature really knows how to fix bath equipment."
- Captions. Write closed captions for your videos. At least YouTube search evaluates the content and if you forgot any important keyword it will likely be included in your transcript.
You furthermore can optimize your videos for other search engines like Google or bing. This is mainly important for howto videos as nobody searches for a video about Hans going to the super market. They work different from YouTube search as they don't interpret audience retention but links to your videos. Basically you want to place as many links as possible to your video in the Internet. The great thing is that they don't only improve your search rank but also bring views from people who follow them.
Easiest is to create social media accounts in addition to Google+ for your channel e.g. Facebook, Twitter, Pinterest, Reddit. You then post links to your videos with the depending keywords e.g. "Have you ever seen that a fish shows you how to repair a toilet?".
G+ and Facebook even have dedicated promotion communities. These won't bring you much views but allow you to drop a link.
Note that Reddit is a bit different. Most of the links you post should lead to other peoples' content or you get banned. You also should only use it to promoteyour best of the best.
There are forums like YTTalk who allow you to drop a link. Be furthermore active in forums that are about your niche and drop links there. For tutorials Yahoo answers has been a great opportunity to place some links in my experience.
Be careful not to Spam or you may be banned and loose a great promotion opportunity.
Write a blog about your video content and link the videos there.
Have your own homepage where you drop video links.
Note that the more quality (real visitors) a page has the more this will boost the video links you drop there. So it can be indeed a good idea to write for other people as long as you can drop a video link (not mentioning the social traffic you will get as a side effect).
As these are all techniques that only help your content to be discovered and don't try to cheat the system they are allowed and so called white hat methods.
There are also black hat method that mainly rely on bot channels, auto generated and stolen content. These are party even illegal so called black hat methods. They usually get your channel banned in the long term.