Looks like the Dell Dimension 2350 has IDE (PATA) connectors and does NOT have SATA connectors.
And only has a bracket to hold 1 HDD.
Always unplug the computer before working inside of it!
Older IDE HDDs are more complicated than the new SATA drives, but here is a quick rundown...
First, check the old drive's jumper pins to check how the old drive is set on the ribbon cable. Sticker on top of the HDD will show you the different setting for the jumpers on a particular HDD. If the old drive is set to CS (cable select), set your new drive's jumper pins to Cable Select as well. If the old HDD is NOT set on CS it will be set as MA (Master). However, on some drives there are 2 different Master settings, one is Master only (only 1 HDD), and the other is Master w/ Slave (2 HDDs). If the old drive is set to Master only, move the jumper to Master w/ Slave, and set new HDD to SL (Slave). If the old HDD only has a Master option, or is already set to Master w/ Slave, leave the jumper alone and set the new HDD to Slave. Basically the HDDs will be CS & CS, OR MA w/ SL & SL, OR MA & SL.
Once you have figured out your jumper pins, connect the 40pin ribbon cable to the new drive. The red part of the ribbon is always closest to the large 4 pin power connector. Also, the slot is keyed (aka fits only 1 way), so do not force the cable. Line up the ribbon connector to the pins on the HDD and firmly slide the connector on to the HDD.
Next, connect a 4pin power connector (Molex). Usually they are white or black and about as wide as your thumb, again the connector is keyed.
Mount the drive into the computer case... usually involves 4 Philips screws.
Plug in computer, turn on computer, load into the BIOS, verify the HDDs are found. If drives are not found, change IDE channels to AutoDetect and scan for the HDDs again. If the HDDs are still not found, either the installation of the HDD was done incorrectly or the new HDD you just bought is faulty (98% chance installer error, 2% chance of bad drive).
If the HDDs are shown in the BIOS, Save the BIOS settings, and then exit BIOS. Load into windows, open Disk Management (right click My Computer, then left click Manage). Initialize, format, and partition your new HDD, usually the New HDD Wizard starts once you load Disk Management after installing a new HDD.