If you are using it on the website, there are a few ways of doing this.
1. There is a search box in the top right hand corner of the page. Type in the name of the person you're searching for, and a list will appear with everyone sharing that name (It's not always easy to to know the difference). There will be a little box beside the name with follow[i on it - click it, and that person will be added to your [i]following[i] list. If you click on the name, it takes you to their profile and will be a box with [i]following[i] on it. Beside that is what looks like a cog. Click on that and the first link is Tweet to @YorkshirePigeon (For example). Type your message in and click the [i]Tweet[i] box, and your message will be sent.
On the left hand side of the page is a box you can type tweets into, It says [i]Compose new Tweet[i]. If you know the Twitter name of the person you want to Tweet to, type it in the box starting @YorkshirePigeon (For example) and a list will appear. Click the name you want (Not too sure if this list is just the people you follow or a general list) and it will fill in the rest of the name. Type your Tweet as normal and then click on the [i]Tweet] button. Job done.
Hope this isn't too complicated.....