I have recently been hired by a local video production company to design, and develop websites for them and there clients. I am confident in my ability to write the website, however being my first job ever in this industry I want to do well and secure my position.

Does anyone have any advice or tips on first starting in this endeavor?

Specify what is involved for each project in writing in consultation with the client and get it signed off by the client. Base your price on that and don't deviate. Additions to the project then come at an increased cost. Scope creep will kill you otherwise.
Set a realistic deadline and stick to it.
Get major milestones in the project signed off as complete by the client (in writing) before moving on.
Basically make sure both you and the client know what is going to be done for how much and make sure they are happy with every phase of the project. Rework due to miscommunication or growing requirements will wipe out your profit on the job.

Specify what is involved for each project in writing in consultation with the client and get it signed off by the client. Base your price on that and don't deviate. Additions to the project then come at an increased cost. Scope creep will kill you otherwise.
Set a realistic deadline and stick to it.
Get major milestones in the project signed off as complete by the client (in writing) before moving on.
Basically make sure both you and the client know what is going to be done for how much and make sure they are happy with every phase of the project. Rework due to miscommunication or growing requirements will wipe out your profit on the job.

Well said...

That is very good advice, thank you. Just a note however, I am taking a hourly salary.

if your client tells you, you're not allowed to use a certain technology, don't go all high and mighty and think: I'll write it in that langauge/framework anyway, because I can make it really good-lookin', or very professional or efficiënt.

if your client tells you not to use something, they most likely have a very good reason for that. they decide on any restrictions, and within that frame, see that you get "the job done". good luck and all the best in your new job. :)

Do the job according to the clients requirement then he will be happy so that you have done a great job for him, And finish the job as soon as possible with good design he will be very happy.

Communicate with the client, there will be a hundred changes in requirements during the development
test run every aspect you can imagine, and those you can't, before it goes live,

I, middle aged, old fashioned,
typify the small company C-levels who will sign your cheques
websites for them and there clients is not the same as websites for them and their clients
and will be the difference between referrals and no referrals,

proof read like a high school English teacher

Define the number of changes you will accept before you start charging more for the extra work.
Don't work for free!

proof read like a high school English teacher

+1. The things my clients send me... It's like they had their eyes closed and fingers taped together when they were typing up content. There are points where I'm sure they've fallen asleep typing, 'cause paragraphs just end mid-sentence.

I also have to second the idea of specifying the amount of revisions you're willing to do for free. Every time you make a change to the site or hit a milestone, the client will look at it and decide there's something they want to change. If you don't set your foot down on how many modifications they're allowed to request, you'll find yourself months later tweaking things you thought you finished a while ago.

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