Amplifying low titer stock can be a little tricky. The most important determinant of success is the general vigor of the particular construct that you have. Some virus constructs replicate very efficiently, and they're easy. Others are not so cooperative.
The Low MOI Infection protocol on my site is the way I'd start.
If you have a volume greater than a couple mL of you stock, then you can go right into a 25 mL culture growing in log phase at a density of about 4-6E5. Stay on the low side of cell density, because your a bit short of virus. Add a mL or two of virus after the cells have gotten into lag phase, and then monitor for growth every day. If you set up a control flask to which you add no virus, interpretation will be easier.
The cells will grow for at least a day or two, doubling each day if they're not yet infected. If you're successful, the infected flask will show two things. First, the cell density will stop increasing around 24-48 hours, preferably below 2.5 E6 while the uninfected cells will continue to increase to 3-6E6, depending on your cell line and medium combination. Second, the infected cells will grow much larger; 20-50% larger diameter, nearly double the volume.
If this happens, you are in business. Pellet the cells and filter the SN through >= 0.45 micron filter. You don't really need to filter, though it's a good practice over time. Filtration will drop your titer some. This new virus stock should be between 3E7 and 3E8 pfu/mL.
If you don't have enough virus stock volume, you can amplify in 6 to 24 well dish or a small culture dish. Add a small number of cells to several wells of the dish (say about 2-5E5 cells to a 6 well dish, adjusted down by area for a smaller well). After they have adhered, remove the medium, and add fresh medium, at least 2 ml to a 6 well dish, probably no more than 4mL. I use TNMFH for growth medium on plates, unless this stock may be used in clinical settings eventually and you need to avoid serum. Serum free commercial media will also work fine.
Add sequentially more virus to each of a series of wells, say 1, 3, 10, 30 and 100 microliters. **Remember** to leave at least one well uninfected as a control. The smaller the volume of stock that you have, the lower the number of cells you want to use so the virus has a chance to catch up with the cells. Incubate at 27C for several days observing the growth daily. The best titer virus stock will be found in the well that grows a confluent or nearly confluent cell layer, but which is clearly inhibited relative to the control. The control should overgrow and become very dense. The uninfected cells should grow to confluency in about 3 or 4 days. Let the cultures go a couple days beyond that point.
Collect the cells and medium from all promising wells. Spin out the cells and transfer the SN to a new tube. Perform a Low MOI infection in a 25 mL shake flask culture.