Warning :
Some videos from web sites like YouTube, Dailymotion, Yahoo!Video or Google Video may be protected by a copyright. Therefore, their use in any moviemaking may be restricted or forbidden. The goal of this tutorial is to teach you how to transcode them in order to import them in Studio. You remain responsible for their use.
Those videos are mostly in an .flv or .mp4 container (for downloading videos in flv or mp4 format, we recommend using one of the tool we propose, KeepVid, YouTube Download Tool or VDownloader or any other firefox plugin like DownloadHelper). We will learn how to transform them to AVI, so that, importing in Studio becomes possible.
Step 1 : Software installation
In this tutorial we will make use of VirtualDub, the famous opensource video processing software developed about 10 years ago by the renowned Avery Lee. Version 1.8.0 or newer of VirtualDub is required. Those with a prior version already installed on their PC will have to re-install it. You can download the latest official version at Virtualdub.org.
It's a simple ZIP file you'll have to unzip wherever you want. Once the files are unzipped, create a new folder called plugins32 in the root directory of VirtualDub. As there is, in fact, no installation of the program in :\Program Files, I recommend that you create a shortcut on the Windows desktop. For this, right-click on VirtualDub.exe and choose Send to, Desktop (create shortcut).
Since the 1.7.x VirtualDub branch and the nearly complete re-write of the code by Avery Lee, VirtualDub can be supplemented by new input plugins to import formats other than AVI. People have begun to develop such plugins. You can find a plugin coded by Moitah for .flv and a plugin coded by Tateu for .mp4 files.
For the .flv, you'll find the plugin at Moitah's web site. You must download the file called FLV_Input_Driver.zip. Unzip it and drag'n drop the file FLVInputDriver.vdplugin into the plugins32 folder of VirtualDub.
For the .mp4, download the file qtvd_bin (install) on our usual download page. After unzip, you'll get a Quicktime.ini which should be drag'n dropped in the root directory of VirtualDub and a Quicktime.vdplugin to drag'n drop into the plugins32 folder of VirtualDub.
Let's start VirtualDub by selecting VirtualDub.exe or launching its shortcut from the desktop. In the Menu File we load our .flv or .mp4 video with Open video file... :

Here, it's very possible you will get this error message :

It's absolutley normal. Indeed, VirtualDub is still based on the VFW (Video For Windows) video architecture. Which means that VirtualDub doesn't find any VFW decoder on your PC able to decode the video stream of your file.
It's time to install a second software called Ffdshow tryouts and which is in fact a kind of universal decoder for audio/video streams. I believe that Ffdshow should be present on every PC for users who wish to be able to read any video format without having to install hazardous codecs pack.
Download the latest Ffdshow version at SourceForge.net. Once downloaded, launch the .exe file. Settings on the 2nd window should be like these :

Complete the installation without changing the default options.
Once the installation is complete, in Start, Programs, ffdshow, open VFW configuration. Control that in the Decoder tab, Codecs, in front of FLV1 and VP6F you have libavcodec. Like this :

If this is not the case, you must hit disabled in front of FLV1 and VP6F and choose libavcodec. Confirm by hitting OK or Apply. All this preparatory work was done to enable the opening of .flv and .mp4 files in VirtalDub.
Step 2 : Framerate modification
The framerate is the number of frames in each second of video. Launch VirtualDub once again and re-load a file like you did before. We must verify the framerate of the video we want to transcode. For that, in Menu File select File Information... :

We get that :

If in front of FPS there's something else than 25 for people using PAL or 29.97 for those using NTSC, you'll have to modify it. Go to Menu Video, Frame Rate... :

In the Frame rate conversion zone, in Convert to fps : put 25 or 29.97 depending on your format and hit OK :

Step 3 : Resizing
Using the same method as for the framerate in Step 2, edit the video resolution. For DV PAL, the picture should be 720x576 and for DV NTSC 720x480. If this is not the case, go to Menu Video, Filters..., Add..., choose the resize filter and hit OK.
In the settings window select Aspect ratio = Disabled, New size = Absolute (pixels) and put 720 x 576 or 720 x 480. In Filter mode choose Lanczos3, which is a resizing algoritm pretty slow but better than others :

Confirm twice by clicking OK. Some of you may have noticed that this method doesn't preserve the original aspect ratio. In order to simplify the tutorial, we will assume that it's not a critical factor.
Step 4 : Video compression
Go to Menu Video, Compression... :

In the window Select video compression select a codec and hit Configure if you want to enter the codec settings area. Hit OK. Note that Full processing mode is selected :

Choosing a codec may be a crucial moment if you want Studio to be able to open your rendered file. It's up to you to make several tests. Xvid or DivX seem to be good choices.
Step 5 : Audio Selection
If there's an audio track in your video, you must select it. Go to Menu Audio, Source audio, Stream 1, and be sure that Direct stream copy is selected :

If there's no audio, select No audio.
Step 6 : File saving
To save the file, go to Menu File, Save as AVI... :

If you get this error warning :

it means that a conflict exists between the codec and the color space of the video in the .flv or .mp4. Such a conflict may frequently occur with DV codecs. It's a little bit too difficult to explain it here, so you'd better go back and choose another compatible codec.
Conclusion :
I'm fully aware that this tutorial may frighten some readers. But I believe that the only way to learn is to practice. The use of all-in-one software is definitely easier, but much less rewarding when at the end you succeed to do the complete job by yourself. And it allows the user to adapt the method to several situations.
Those who use only SmartMovie in Studio avoid many troubles, but many personal satisfactions too. Keep going ! 
{Thanks to Loosecannon for the fine tuning}